## Numerical analysis reports

The Numerical Analysis group published a series of reports detailed below. Some of these reports are available online. This series has now been subsumed into the Preprint series and the Mathematics Report series:

- 2007
- 2006
- 2005
- 2004
- 2003
- 2002
- 2001
- 2000
- 1999
- 1998
- 1997
- 1996
- 1995
- 1994
- 1993
- 1992
- 1991
- 1990
- 1989
- 1988
- 1987
- 1986
- 1985
- 1984
- 1983
- 1982
- 1981
- 1980

### 2007

1/2007 Weak constraints in four-dimensional variational (PDF-985Kb)

L.R. Watkinson, A.S. Lawless, N.K. Nichols and I. Roulstone

2/2007 Towards data assimilation for high resolution nested models (PDF-133Kb)

G.M. Baxter, S.L. Dance, A.S. Lawless, N.K. Nichols and S.P. Ballard

3/2007 Correlated observation errors in data assimilation (PDF-606KB)

L.M. Stewart, S.L. Dance and N.K. Nichols

4/2007 Modelling of forecast errors in geophysical fluid flows (PDF-181KB )

R.N. Bannister, D. Katz, M.J.P. Cullen, A.S. Lawless and N.K. Nichols

5/2007 Approximate Gauss-Newton methods using reduced order models (PDF-180KB)

A.S. Lawless, N.K. Nichols, C. Boess, A. Bunse-Gerstner

6/2007 Existence and properties of solutions for neural field equations (PDF-276KB)

P. beim Graben and R. Potthast

7/2007 Modelling the diurnal variability of sea surface temperatures (PDF-1.6MB)

S. Pimentel, K. Haines, N.K.Nichols

8/2007 The assimilation of satellite derived sea surface temperatures into a diurnal cycle model (PDF-648KB)

S. Pimentel, K. Haines, N.K.Nichols

9/2007 Orthogonality sampling for object visualization (PDF-829MB)

R. Potthast

10/2007 Simple models of changing bathymetry with data assimilation (PDF-338KB)

P.J. Smith, M.J. Baines, S.L. Dance, N.K. Nichols and T.R. Scott

### 2006

1/2006 Use of potential vorticity for incremental data assimilation

M.A. Wlasak, N.K. Nichols & I. Roulstone

2/2006 Using constraint preconditioners with regularized saddle-point problems

H.S. Dollar, N.I.M. Gould, W.H.A. Schilders & A.J. Wathen

3/2006 Constraint-style preconditioners for reqularized saddle point problems

H.S. Dollar

4/2006 Information content of spatially correlated observation errors

L.M. Stewart, S.L. Dance & N.K. Nichols

5/2006 A note on permutations for quadratic programming problems

H.S. Dollar

6/2006 Unbiased ensemble square root filters

D.M. Livings, S.L. Dance, and N.K. Nichols

7/2006 A Galerkin boundary element method for high frequency scattering by convex polygons

S.N.Chandler-Wilde and S. Langdon

8/2006 A comparison of potential vorticity-based and vorticity-based control variables

D. Katz, A.S. Lawless, N.K. Nichols1, M.J.P. Cullen and R.N. Bannister

9/2006 Small- and waiting-time behaviour of the thin-film equation

J.F. Blowey, J.R. King and S.Langdon

10/2006 Using model reduction methods within incremental 4D-Var

A.S.Lawless, N.K.Nichols, C.Boess and A. Bunse-Gerstner

11/2006 Scale analysis of observational information in data assimilation

G.M. Baxter, S.L. Dance, A.S. Lawless and N.K. Nichols

12/2006 Convergence and numerics of a multi-section method for scattering by three-dimensional rough surfaces

Eric Heinemeyer, Marko Lindner and Roland Potthast

13/2006 On source analysis by wave splitting with applications in inverse scattering of multiple obstacles

Fahmi Ben Hassen, Jijun Liu and Roland Potthast

### 2005

1/2005 A cell by cell adaptive mesh Lagrangian scheme for the numerical solution of the Euler Equations

J. M. Morrell

2/2005 Additive Schwarz preconditioning for p-version triangular and tetrahedral finite elements.

J. Schoeberl, J.M. Melenk, C. Pechstein, and S. Zaglmayr

3/2005 Fast algorithms for setting up the stiffness matrix in hp-FEM: a comparison.

T. Eibner, J.M. Melenk

4/2005 A singular vector perspective of 4D-Var: The spatial structure and evolution of baroclinic weather systems

C. Johnson, B. J. Hoskins, N. K. Nichols and S. P. Ballard

5/2005 Inner loop stopping criteria for incremental four-dimensional variational data assimilation

A.S. Lawless and N.K. Nichols

6/2005 Efficient evaluation of highly oscillatory acoustic scattering surface integrals

M. Ganesh, S. Langdon, I.H. Sloan

7/2005 A collocation method for high frequency scattering by convex polygons

S. Arden, S.N. Chandler-Wilde, S. Langdon

### 2004

1/2004 A singular vector perspective of 4D-VAR: Filtering and interpolating..

C. Johnson, N.K. Nichols and B.J. Hoskins

2/2004 An investigation of incremental 4D-Var using non-tangent linear models

A.S. Lawless, S.Gratton and N.K. Nichols

3/2004 Approximate iterative methods for variational data assimilation

A.S. Lawless, S. Gratton and N.K. Nichols

4/2004 Variational data assimilation for Hamiltonian problems

L.R. Stanton, A.S. Lawless, N.K. Nichols and I. Roulstone

5/2004 Very large inverse problems in atmosphere and ocean modelling

C. Johnson, N.K. Nichols and B.J. Hoskins

6/2004 Preconditioners for inhomogenous anisotropic problems in spherical geometry

D.E.Brown, N.K.Nichols and M.J.Bell

7/2004 A ghost fluid, moving finite volume plus remap method for compressible Euler flows

D.A. Bailey, P.K. Sweby and P. Glaister

8/2004 Generation of Arbitrary Lagragian-Eulerian (ALE) Velocities, based on monitor functions, for the solution of compressible flow equations

B.V. Wells, M.J. Baines and P. Glaister

9/2004 Approximate Gauss-Newton methods for nonlinear least squares problems

S.Gratton, A.S. Lawless and N.K. Nichols

10/2004 A local error analysis of the boundary concentrated FEM

T. Eibner and J.M. Melenk

11/2004 On Approximation in Meshless Methods

J.M. Melenk

12/2004 On Approximation in Meshless Methods

T. Eibner and J.M. Melenk

### 2003

1/2003 Lagrange-Remap methods for the Euler Equations for single and multi gas flow..

D.A. Bailey

### 2002

1/2002 Four Dimensional Variational Data Assimilation in the Presence of Idealised Rapidly Growing Weather Systems

C Johnson, N.K. Nichols, B.J. Hoskins, S.P. Ballard & A.S. Lawless

2/2002 A moving mesh method for non-linear parabolic problems

K.W. Blake & M.J. Baines

3/2002 Linearising the Kepler Problem for 4D-Var Data Assimilation

Laura Stanton

4/2002 Crowded - Macroscopic and microscopic models for pedestrian dynamics

Penny Marno

5/2002 On the numerical solution of selected integrable nonlinear wave equations

Malachy McConnell

### 2001

1/2001 Numerical solution of hyperbolic systems of conservation laws with source terms - Part I

A C Lemos, M J Baines and N K Nichols

2/2001 Numerical modelling of traffic on the M25 motorway: Part 1

Joanne Morgan

3/2001 Numerical modelling of traffice on the M25 motorway: Part II

Joanne Morgan

4/2001 A comparison of two methods for developing the linearization of a shallow water model

A S Lawless, N.K.Nichols and S. P Ballard

### 2000

1/2000 Mesh movement by mass conservation

K.W. Blake

2/2000 Numerical Formulations for approximating the Equations Governing Bed-Load Sediment Transport in Channels and Rivers.

J. Hudson and P.K. Sweby

3/2000 A new method for solving the 2-D advection equation

A. Laird

4/2000 Finite differences applied to stochastic problems in pricing derivatives

S. Christodoulou

5/2000 Galerkin methods for coupled integral equations

S.H. Man

6/2000 A marker and cell solution of the incompressible Navier-Stokes equations for free surface flow

B. Weston

7/2000 The solution of steady PDEs on adjustable meshes in multidimensions using local descent methods

M.J. Baines

8/2000 Multidimensional least squares fluctuation distribution schemes with adaptive mesh movement for steady hyperbolic equations

M.J. Baines, S.J. Leary and M.E. Hubbard

### 1999

1/99 On the accuracy of one-dimensional models of steady converging/diverging open channel flows.

M.E. Hubbard

2/99 Numerical techniques for the Shallow Water Equations.

J. Hudson

3/99 Flux difference splitting and the balancing of source terms and flux gradients

M.E. Hubbard and P.Garcia-Navarro

4/99 Aspects of multidimensional upwinding: time-dependent nonlinear systems, source terms, spherical geometries and three-dimensional grid adaptation

M.E. Hubbard

5/99 High order advection schemes: automatic generation

R. Lashley

6/99 Robust eigenstructure assignment in quadratic matrix polynomials: nonsingular case

N.K. Nichols & J Kautsky

7/99 Godunov Methods

P.K. Sweby

8/99 The use of moving grids in contour zoning

K.W. Blake

9/99 Adjoint methods in data assimilation for estimating model error

A.K. Griffiths and N.K. Nichols

10/99 High Order Advection Schemes; Automatic Generation.

R.K. Lashley

11/99 Moving finite element, least squares and finite volume approximations of steady and time-dependent PDEs in multidimensions

M.J. Baines

### 1998

1/98 Multidimensional upwind fluctuation distribution schemes for scalar time dependent problems

M.E. Hubbard and P.L. Roe

2/98 Multidimensional slope limiters for MUSCL-type finite volume schemes.

M.E. Hubbard

3/98 Bifurcation analysis of eigenstructure assignment control in a simple nonlinear aircraft model

L.P. Gibson, N.K. Nichols and D.M. Littleboy

4/98 Application of variational data assimilation to the Lorenz equations using the adjoint method

M.A. Wlasek and N.K. Nichols

5/98 Adjoint Methods for Treating Model Error in Data Assimilation

A.K. Griffith and N.K. Nichols

6/98 Fluctuation distribution schemes on adjustable meshes for scalar hyperbolic equations

M.J. Baines and S.J. Leary

7/98 Interim report on the application of non-linear optimal control techniques in open channel water management

I. Villanueva

8/98 Multidimensional slope limiters for MUSCL-type finite volume schemes II - on improving existing unstructured grid techniques

M.E. Hubbard

9/98 Numerical methods for the Emden-Fowler equations

A.C. Lemos, M.J. Baines and N.K. Nichols

### 1997

1/97 Conservative multidimensional upwinding for the steady two-dimensional shallow water equations.

M.E. Hubbard and M.J. Baines

2/97 On variational and least squares methods with adjustable nodes

M.J. Baines

3/97 Least squares, equidistribution and conservation

M.J. Baines

4/97 Interface tracking using Eulerian methods with a Lagrangian phase

P. Sims

5/97 Modal coupling in linear control systems using robust eigenstructure assignment

D.M. Littleboy and N.K. Nichols

6/97 Least squares minimisation and a steepest descent method for the scalar advection equation and a Cauchy-Riemann system on an adaptive grid.

M.E. Hubbard

7/97 A collection of MATLAB subroutines for the implementation of damped algebraic Riccati equations

J.J. Hench

8/97 A note on duality in a scalar hyperbolic equation

M.J. Baines

9/97 Numerical experiments on the solution of a scalar advection equation by least squares on optimal grids

S.J. Leary

10/97 Variational data assimilation: a study

M.A. Wlasek

11/97 An upwind scheme for the 2D shallow water equations with applications

P. Brufau

### 1996

1/96 Evaluation of the proposed new unified model scheme vs the current unified model scheme on the shallow water equations

A.J. Malcolm

2/96 Accounting for model error in data assimilation using adjoint methods

A.K.Griffith and N.K.Nichols

3/96 Optimal strategies for the control of wave energy converters with various power-take-off mechanisms

N.K. Nichols and A. Crossley

4/96 Numerical variational techniques on adjustable meshes

M.J. Baines

5/96 A note on damped algebraic Riccati equations

C-Y. He, J.J. Hench and V. Mehrmann

6/96 A first principles derivation of a simple non-linear aerodynamic model

J.J. Hench and N.K. Nichols

7/96 Approximate solutions of partial differential equations on optimal meshes using variational principles

M.J. Baines

### 1995

1/95 Computation of the net present value of a reservoir with uncertain data..

M.P. Dainton and N.K. Nichols

2/95 Comparisons of some steady state Saint-Venant solvers for some test problems with analytic solutions.

I. MacDonald, M.J. Baines, N.K.Nichols and P.G. Samuels

3/95 Steady open channel test problems with analytic solutions.

I. MacDonald, M.J. Baines, N.K. Nichols and P.G. Samuels

4/95 Conservative multidimensional upwinding for the shallow water equations.

M.E. Hubbard, P. Garcia-Navarro and M.J. Baines

5/95 A dynamical approach study of some explicit and implicit and TVD schemes and their convergence to steady-state solutions

P.A. Burton and P.K. Sweby

6/95 Use of a discrete norm in best piecewise constant approximation of continuous functions on irregular grids

M.J. Baines

7/95 An MFE-like method for best approximation

M.J. Baines

8/95 Properties of a grid movement algorithm

M.J. Baines

9/95 Grid adaptatin for 1-D unsteady problems

P. Garcia-Navarro

10/95 Direct computation of stochastic flow in reservoirs with uncertain parameters

M.P. Dainton, M.H. Goldwater, N.K. Nichols

11/95 Improving second moment conservation in semi-Lagrangian methods

A. Priestley and P. Garcia-Navarro

12/95 Comparison of explicit and implicit TVD schemes for the shallow water equations on a sphere

A.J. Crossley

13/95 The use of variational principles in determining approximations to continuous and discontinuous shallow water flows

S.L. Wakelin, M.J. Baines and D. Porter

### 1994

1/94 The state estimation of flow demands in gas networks from sparse pressure telemetry.

N.K. Nichols and S.M. Stringer

2/94 A numerical method for the computation of the analytic singular value decomposition.

S.J.G. Bell and N.K. Nichols

3/94 Genuinely multidimensional upwinding for the 2D shallow water equations.

P. Garcia-Navarro, M.E. Hubbard and A. Priestley

5/94 Gaussian elimination with pivoting for multi-diagonal systems

C.I. Christov

6/94 Test problems with analytic solutions for steady open channel flow.

I. MacDonald

7/94 Analysis and computation of steady open channel flow using a singular perturbation.

I. MacDonald, M.J. Baines and N.K. Nichols

8/94 Grid adaptation and multidimensional upwinding.

M.E. Hubbard

9/94 Direct solution of reservoir flow equations with uncertain parameters.

M.P. Dainton, M. Goldwater, N.K. Nichols

10/94 Data assimilation using optimal control theory..

A.K. Griffith and N.K. Nichols

11/94 Data assimilation using observers.

A.K. Griffith and N.K. Nichols

### 1993

1/93 On algorithms for best L2 fits to continuous functions with variable nodes.

M.J. Baines

2/93 A hybrid central/upwind approach to the solution of the one dimensional Euler equations.

M.E. Hubbard

3/93 Error measurements for semi-Lagrangian schemes.

C.J. Smith

4/93 The Lagrange-Galerkin method: quadrature is dead, long live inexact integration

A. Priestley

5/93 Application of the Taylor-Galerkin method to transport problems in subsurface hydrology.

K.J. Neylon

6/93 A conservative and shape-preserving semi-Lagrangian method for the solution of the shallow water equations.

P. Garcia-Navarro and A. Priestley

7/93 A survey of genuinely multi-dimensional upwinding techniques.

M.E. Hubbard

8/93 Numerical experiences with Bi-CGSTAB on an advection-diffusion..

K.J. Neylon

9/93 Numerical methods for the solution of systems of uncertain steady-state differential equations.

M.P. Dainton

10/93 The application of an implicit TVD method for water flow modelling in channels and pipes.

P. Garcia-Navarro and A. Priestley

11/93 Integral operators of Sturm-Liouville type

D. Porter and D.S.G. Stirling

13/93 Dynamic-algebraic equations and control system design

N.K. Nichols

### 1992

2/92 A quasi-conservative version of the semi-Lagrangian advection scheme

A. Priestley

3/92 The implementation of a direct domain decomposition method on a small transputer system.

K.J. Neylon

4/92 Variational principles for free surface flows.

S.L. Wakelin

5/92 MASTERFUL - Monotonic Adaptive Solutions of Transient Equations using Recovery, Fitting, Upwinding and Limiters.

M.J. Baines

6/92 The rate of convergence of the viscosity method for a nonlinear hyperbolic system

Y.G. Lu, P.K. Sweby and K. Chen

7/92 Backwater analysis for channel flows and side-weirs using IDES

A. Priestley

8/92 The application of Roe's scheme to two problems of engineering interest

A. Priestley

9/92 Steady flow in channels with decreasing discharge: theory and computation

D. Porter and A. Priestley

10/92 Approximations to channel flows using variational principles.

S.L. Wakelin

11/92 An analysis of some higher-order triangular elements and their susceptibility to hourglassing in Lagrangian fluid simulations

A. Priestley

12/92 Optimal growth strategies when mortality and production rates are size-dependent

N. Perrin, R.M. Sibly and N.K. Nichols

### 1991

1/91 The Taylor Galerkin method for advection on the sphere

A. Priestley

2/91 On the relationship between the moving finite element procedure and best piecewise linear L2 fits

M.J. Baines

3/91 Regularization of descriptor systems by derivative and proportional state feedback

N.K. Nichols, A Bunse-Gerstner and V. Mehrmann

4/91 Equidistribution and the Legendre transformation

M.J. Baines and S.L Wakelin

5/91 An investigation of the form of an optimal controller in a tidal power generation scheme with two controls

Z.G. Xu and N.K. Nichols

6/91 Hydrodynamic modelling and optimal control of tidal power schemes in long estuaries

Z.G. Xu and N.K. Nichols

7/91 On spurious asymptotic numerical solutions of 2x2 systems of ODEs.

P.K. Sweby and H.C. Yee (NASA)

8/91 Numerical methods for optimal control problems with state constraints

S. Lyle and N.K. Nichols

9/91 The Taylor-Galerkin method for the shallow water equations on the sphere

A. Priestley

10/91 On time step selection for solving 1D nonlinear diffusion equations

K.Chen, M.J. Baines and P.K. Sweby

11/91 An adaptive time stepping strategy for the ASWR semiconductor diffusion model simulator

K.Chen, M.J. Baines and P.K. Sweby

12/91 The Legendre transformation and grid generation in two dimensions..

S.L. Wakelin

13/91 Black oil reservoir simulation in 1-D via the higher order Godunov method.

E.M. Dicks

14/91 On unconditionally linearly stable centred and upwind semi-implicit methods for convection and convection diffusion problems

M.J. Baines

15/91 PLAGIARISM: Priestley's LAgrange Galerkin Is A Really Interesting Sheme & Monotone. The multidimensional monotone and nearly conservative Lagrange-Galerkin method

A. Priestley

16/91 Shock fitting for the 2D Euler equations

P.D. Arnold

### 1990

1/90 A survey of some data-dependent criteria for triangular tessellations using fixed nodes

A. Malcolm

2/90 A comparison of the directional difference scheme and Roe's scheme for the approximate solution of transient flow of an ideal gas in a pipe

S. Emmerson

3/90 On spurious steady-state solutions of explicit Runge-Kutta schemes

P.K. Sweby, H.C. Hee (NASA) and D.F. Griffiths (Dundee)

5/90 A quasi-Riemann method for the solution of one-dimensional shallow water flow

A. Priestley

6/90 On best piecewise linear L_2 fits with adjustable nodes

M.J. Baines and N. Carlson (Univ. of California)

7/90 Robust pole assignment in systems subject to structured perturbations

J. Kautsky (Flinders University) and N.K. Nichols

8/90 The form of optimal controllers for tidal-power-generation-schemes

T.P. Andrews, N.K. Nichols and Z. Xu

9/90 Shock structure for physical gases

P.C. Samuels

10/90 A search for new finite elements to be used in conjunction with free-Lagrangian methods

A. Priestley

11/90 Moving finite element procedures and overturning solutions

M.J. Baines and C.P. Reeves

12/90 On best piecewise constant L_2 fits with adjustable nodes

M.J. Baines

14/90 Conjugate gradient methods for the solution of boundary integral equations on a piecewise smooth boundary

K. Chen

15/90 On piecewise linear and constant L_2 fits with adjustable nodes in 2-D

M.J. Baines

16/90 Data-dependent criteria for nodal placement with fixed connectivity in triangular grids.

A. Malcolm

17/90 On stability radius of generalized state-space systems.

R. Byers and N.K. Nichols

18/90 Experiments with 2D shock fitting for the Euler equations

P.D. Arnold

### 1989

1/89 Shocked flow in nozzles

J. Wixcey

2/89 The spectral Lagrange Galerkin method for the atmospheric transportation of pollutants

A. Priestley

3/89 A practical model for heavy oil recovery

R. Brown

4/89 The spectral Lagrange-Galerkin method for the atmospheric transportation of pollutants. Part II. Stability of the non-exact integration

A. Priestley

5/89 Moving finite elements and approximate Legendre transformations

M.J. Baines

6/89 Source terms and conservation laws: a preliminary discussion

P.K. Sweby

7/89 The application of optimal control theory to tidal-power-generation problems

R. Moody

8/89 The numerical solution of one-dimensional shallow-water problems using the Taylor-Galerkin method

R. Moody

9/89 The spectral Lagrange-Galerkin method for the atmospheric transportation of a pollutant! Part III. The atmospheric transportation of a pollutant!

A. Priestley

10/89 Foundations for the study of systems of conservation laws with limiting diffusion

P. Samuels

11/89 On derivative and proportional feedback design for descriptor systems

A. Bunse-Gerstner, Volker Mehrmann, N.K. Nichols.

12/89 Shock behaviour and diffusion

P. Samuels

13/89 Roe-type schemes for super-critical flows in rivers

A. Priestley

14/89 On stability of descriptor systems

R. Byers, and N.K. Nichols

15/89 On the convergence of the Ritz-Galerkin technique for solving two-dimensional optimal shape problems

S. Lyle and N.K. Nichols

16/89 Inequality constrained finite elements and conjugate gradients

N.R.C. Birkett

17/89 A comparision between two moving finite element methods

C.P. Reeves

### 1988

1/88 Shock-modelling with body-fitted meshes using a local parameterisation of the equation of state

P. Glaister

2/88 A survey of operator splitting applied to upwind differencing

J.J. Barley

3/88 Robust pole assignment in singular control systems

J. Kautsky, N.K. Nichols and E.K.-W. Chu

4/88 Weak non-symmetric shocks in one-dimension

P. Samuels

5/88 Comments on the numerical integration of a class of singular perturbation problems

N.K. Nichols

6/88 Interfacing of an oxidation model with the two-dimensional Moving Finite Element Model of dopant diffusion

N.S. Cooper

7/88 An analysis of properties of the shock tip in two-dimensional steady compressible flow

P. Samuels

8/88 Optimisation of steam injection into an oil reservoir

R. Brown

9/88 Roe's scheme, Euler equations, Cartesian grids, non-Cartesian geometries, rigid walls and there's more

A. Priestley

10/88 Stability of descriptor systems.

R. Byers (Univ of Kansas) and N.K. Nichols

11/88 On the solution of nonlinear diffusion equations

M.J. Baines

12/88 Compressible flow in ducts - analytic aspects

J. Wixcey

13/88 Compressible flow in ducts - variational aspects

J. Wixcey

14/88 Compressible flow in ducts - an adaptive grid method

J. Wixcey

15/88 Numerical approximation of the Legendre transformation

M.J. Baines

16/88 Roe's scheme, Euler equations, Cartesian grids, non-Cartesian geometries, rigid walls - The continuing story

A. Priestley

17/88 Output feedback via state feedback and least squares

S. Slade

18/88 The implementation of boundary conditions in the application of Roe's scheme to aeronautical flows on Cartesian grids

A. Priestley

### 1987

1/87 Stability properties of some algorithms for the solution of non-linear dynamic vibration equations

W.L. Wood and M.E. Oduor

2/87 An approximate Riemann solver for compressible flows with axial symmetry

P. Glaister

3/87 A numerical simulation of one-dimensional dopant diffusion in oxidising silicon

R.O. Moody and C.P. Please

4/87 A two dimensional algorithm for the non-linear equations of gas dynamics employing operator splitting

J.J. Barley

5/87 Moving finite element modelling of the 2-D shallow water equations

R.D. Alstead

6/87 Second order difference schemes for hyperbolic conservation laws with source terms

P. Glaister

7/87 Data-dependent grids

P.K. Sweby

8/87 Roe type schemes for the 2-D shallow water equations

A. Priestley

9/87 Difference schemes for the shallow water equations

P. Glaister

10/87 A constrained moving finite element method for moving boundary problems

R.O. Moody

11/87 A two-dimensional compressible solver incorporating body-fitted coordinates

P. Glaister

12/87 Moving finite envelopes

M.J. Baines

13/87 Some observations on the moving finite element method and its implementation

Peter K. Sweby

14/87 Roe's scheme, Euler equations, Cartesian grids, non-cartesian geometries, rigid walls and all that

A. Priestley

15/87 On the efficient solution of the Euler equations with real gases

P. Glaister

16/87 An implicit regridding algorithm with an underlying fixed grid, for front, shock or boundary tracking

D.E. Heath

### 1986

1/86 Latching control for the point-absorber wave-power device

Ruth E. Hoskin and Nancy K. Nichols

2/86 Projections and constraints II

M.J. Baines

4/86 Shock modelling on irregular grids

P. Glaister

5/86 A transformation to assist numerical solution of diffusion equations

C.P. Please and P.K. Sweby

6/86Robustness in partial pole placement

N.K. Nichols

7/86 An approximate linearised Riemann solver for the Euler equations in one dimension with a general equation of state

P. Glaister

8/86 A numerical study of a non-Newtonian flow problem

M.F. Webster, E.E. Suli and K.W. Morton

9/86 Non-linear optimal control of tidal power schemes in long estuaries

N.R.C. Birkett

12/86 An approximate Riemann solver for three-dimensional multifluid flows using operator splitting

P. Glaister

14/86 Bordered matrices and applications to ergodic Markov chains

King-Wah Eric Chu

15/86 A note on the pole assignment of q-D linear systems

K.-w. E. Chu

16/86 On the controllability of descriptor systems

K.-w. E. Chu

17/86 Numerical simulation of hot fluid injection into porous media

D.E. Heath

18/86 A review of the Lanczos method applied to generalised non-symmetric eigenproblems

S. Slade

19/86 Moving finite elements: regularisation techniques

M.J. Baines

### 1985

1/85 On approximate solutions of time-dependent partial differential equations by the moving finite element method

M.J. Baines

2/85 Nonlinear optimal control problems in tidal power calculations

N.R.C. Birkett

3/85 Superconvergent estimation of the gradient from linear finite element approximations on triangular elements

Nick Levine

4/85 Moving finite element modelling of compressible flow

M.J. Baines and A.J. Wathen

5/85 Generalizations of the Bauer-Fike theorem

King-wah Eric Chu

8/85 Flux difference splitting techniques for the Euler equations in non-cartesian geometry

P. Glaister

9/85 Local moving finite elements

M.J. Baines

10/85 The solution of the matrix equations AXB - CXD = E and (YA - DZ, YC - BZ) = (E,F)

King-wah Eric Chu

11/85 Exclusion theorems and the perturbation analysis of the generalized eigenvalue problem

King-wah Eric Chu

12/85 Moving finite elements for nonlinear diffusion problems in one and two dimension

I.W. Johnson

13/85 A numerical study of incompressible flow problems of non-newtonian or turbulent type

M.F. Webster

14/85 A semi-robust pole assignment algorithm for linear state feedback

King-wah Eric Chu

15/85 Moving finite elements: projections and constraints

M.J. Baines

16/85 Singular value and generalised singular value decompositions and the solution of linear matrix equations

King-wah Eric Chu

17/85 A moving finite element solution of the one-dimensional Crank-Gupta problem

R.O. Moody

18/85 Benchmark problems in fluid flow modelling

M.F. Webster and P.K. Sweby

19/85 On matching the SSpj and GNpj algorithms

W.L. Wood

20/85 Mobile finite elements

M.G. Edwards

### 1984

1/84 A fully two-dimensional finite difference method on a regular grid for systems of conservation laws

M.J. Baines

2/84 The hole-pressure problem

M.F. Webster

3/84 The moving finite element method for the viscous Burgers' equation

I.W. Johnson

4/84 A numerical algorithm for the most economical structural synthesis of linear control systems

King-wah Eric Chu

5/84 Robust pole assignment in linear state feedback

J. Kautsky, N.K. Nichols and P. Van Dooren

6/84 Pointwise logarithm-free error estimates for finite elements on linear triangles

Nick Levine

7/84 Robust multiple eigenvalue assignment by state feedback in linear systems

J. Kautsky and N.K. Nichols

8/84 Regularity and robust pole assignment in singular control systems

J. Kautsky, N.K. Nichols and E. K-W. Chu

9/84 A flux limiter based on Fromm's scheme

M.J. Baines and P.K. Sweby

10/84 Comparison of some single-step methods for the numerical solution of the structural dynamic equation

S.N. Penry and W.L. Wood

11/84 On the schemes of Jameson, Davis & Roe

M.G. Edwards

### 1983

1/83 Numerical algorithms for the non-linear scalar wave equation

M.J. Baines

2/83 Robust eigenstructure assignment in state feedback control

J. Kautsky and N.K. Nichols

3/83 The general linear problem of tidal power generation with non-linear head-flow relations

N.R.C. Birkett and N.K. Nichols

4/83 OTEP-2 Optimal train energy programme mark 2

Jaroslav Kautsky and Nancy K. Nichols

5/83 On the structure of the moving finite element equations

A.J. Wathen and M.J. Baines

6/83 Superconvergent recovery of the gradient from piecewise linear finite element approximations

Nick Levine

7/83 Finite element methods for non-self-adjoint elliptic and for hyperbolic problems: optimal approximations and recovery techniques

K.W. Morton

8/83 Optimal control problems in tidal power generation

N.R.C. Birkett and N.K. Nichols

9/83 Recent developments in finite element methods for fluid dynamics problems

K.W. Morton

10/83 Two dimensional shock recognition and Roe's scheme

M.J. Baines

11/83 Optimal recovery and defect correction in the finite element method

J.W. Barrett, G. Moore and K.W. Morton

### 1982

1/82 Finite element method for inviscid compressible fluid using Clebsh variables

Edward Detyna

2/82 Noise problems with ephemeral streams in aquifer models

B.J. Connorton and W.L. Wood

3/82 Generalised Galerkin methods for steady and unsteady problems

K.W. Morton

4/82 Moving finite elements and applications to some problems in oil reservoir modelling

A. Wathen

5/82 Shock capturing, fitting and recovery

K.W. Morton

6/82 A modification of Roe's scheme for entropy satisfying solutions of scalar non-linear conservation laws

P.K. Sweby

8/82 Finite element method with Clebsch representation

Edward Detyna

9/82 Towards a large timestep algorithm for systems of conservation laws: preliminary results ignoring interactions

R.J. Leveque

10/82 Stress sampling points for linear triangles in the finite element method

N. Levine

11/82 Error analysis and numerical experiments for Petrov-Galerkin methods

B.W. Scotney

12/82 A further look at Newmark Houbolt etc. time stepping formulae

W.L. Wood

### 1981

1/81 A high order monotonicity preserving algorithm on an irregular grid for non-linear conservation laws

P.K. Sweby

2/81 The boundary integral method for steady compressible flow in two dimensions

M.G. Hill

3/81 Finite element methods for non-self-adjoint problems

K.W. Morton

4/81 Numerical algorithms for the solution of conservation laws in two and three dimensions

M.J. Baines

5/81 Quasi-variational inequalities related to flow through an anisotropic porous medium

A.W. Craig

6/81 Convergence of Roe's scheme for the non-linear scalar wave equation

P.K. Sweby and M.J. Baines

7/81 Modelling 2-layer rotating flows

J.W. King

8/81 Convergence of Roe's scheme for the general non-linear scalar wave equation

P.K. Sweby and M.J. Baines

9/81 Smoothed histogram modification for image processing

Jaroslav Kautsky, Nancy K. Nichols and David L.B. Jupp

### 1980

1/80 Smooth regrading of discretized data

Jaroslav Kautsky and Nancy K. Nichols

2/80 A numerical algorithm for the solution of systems of conservation laws in two dimensions

M.J. Baines

3/80 Cost-efficiency study of various methods for solving the seepage through dam problem using variational inequalities

A.W. Craig and W.L. Wood

4/80 Optimal Petrov-Galerkin methods through approximate symmetrisation

J.W. Barrett and K.W. Morton

6/80 Rapid elliptic solvers (the final instalment?)

Edward Detyna

7/80 Numerical solution of an elastic boundary-layer problem using a multiple shooting technique

Roland England

8/80 Optimal resource depletion: free end time problems

D.N. Burghes, S. Lyle and N.K. Nichols