Reports pre 1995

Numerical Analysis Group Research Reports 1984-1994

Numerical Analysis Group Research Reports are informal reports of work in progress, or are preprints of papers submitted for publication elsewhere. The following list contains the Research Reports of the years 1984 to 1994 only. Most of this reports are not available electronically but can be scanned on request.

There is a separate list of reports from 1995 onwards.

Numerical Analysis Group Research Reports are printed as A5 booklets. Please contact the Numerical Analysis Group Administrator to find out about the availability of any reports listed below.

NA-84/1
Generalised Galerkin methods for hyperbolic problems,
K W Morton
NA-84/2
Convergence analysis of discretisation methods for nonlinear first kind Volterra integral equations,
R Jeltsch, S McKee, J Dixon
NA-84/3
Order h² convergence of a singular two-point boundary value problem,
G J Shaw, S McKee, M M Chawla
NA-85/1
A unified analysis of discretisation methods for Volterra-type equations,
J Dixon
NA-85/2
Nonlinear singular Volterra equations,
A Stuart, J Norbury
NA-85/3
A comparison of flux-limited difference methods and characteristic Galerkin methods for shock modelling,
P K Sweby, K W Morton
NA-85/4
Generalised reducible quadrature methods for Volterra integral and integro-differential equations,
J Dixon
NA-85/5
Multistep multiderivative methods for Volterra integro-differential equations,
M Meneguette, S McKee, M Favaro
NA-85/6
A continuation procedure for high Rayleigh number flows,
J S Rollett, S Sivaloganathan
NA-85/7
A class of implicit moving boundary problems,
A Stuart
NA-85/8
Parabolic partial differential equations with discontinuous forcing terms,
A M Stuart, J Norbury
NA-85/9
On characteristic Galerkin and Lagrange-Galerkin method,
K W Morton
NA-85/10
Existence and uniqueness of weak solutions to buoyancy driven cavity problem,
S Sivaloganathan
NA-85/11
Recovery of fluid flow fields,
D C Handscomb
NA-85/12
Stresses and displacements around a cylindrical cavity,
M B Reed
NA-85/13
Volterra integral equations and a new Gronwall inequality: Part I The linear case,
A M Stuart, J Norbury
NA-85/14
Volterra integral equations and a new Gronwall inequality: Part II The nonlinear case,
A M Stuart, J Norbury
NA-85/15
On the uniform convergence of a collocation method for a class of singular integral equations,
J Cuminato
NA-86/1
A comparison of cell centre and cell vertex schemes for the steady Euler equations,
M F Paisley
NA-86/2
The stability of a simple IBVP,
N A Burgess
NA-86/3
Convergence analysis of the Lagrange-Galerkin method for the Navier-Stokes equations,
E Süli
NA-86/4
Mollifiers in function spaces,
E Süli
NA-86/5
Characteristic Galerkin methods for scalar conservation laws in one dimension,
K W Morton, P N Childs
NA-86/6
Galerkin finite element methods and their generalisations,
K W Morton
NA-86/7
Symmetry breaking in elliptic systems,
C J Budd
NA-86/8
The stability of an approximation to the 1D shallow water equations,
N A Burgess
NA-86/9
Cell vertex methods and shock fitting for the steady Euler equations,
M F Paisley
NA-86/10
The numerical solution of a model of skin diffusion using SPRINT,
W L Seward, M Rees, T Murdoch
NA-86/11
Petrov-Galerkin methods for parabolic convection-diffusion problems,
W Wei
NA-86/12
A nonlinear weakly singularity Volterra integro-differential equation arising from a reaction-diffusion study in a small cell,
J Dixon
NA-86/14
Stability analysis of the Lagrange-Galerkin method with non-exact integration,
E Süli, A Priestley, K W Morton
NA-86/15
Uniform convergence of a collocation method for the numerical solution of Cauchy-type singular integral equations,
J Cuminato
NA-86/16
Infinite elements for self-adjoint problems,
T Murdoch
NA-86/17
An error bound for the product approximation of nonlinear problems in the finite element method,
T Murdoch
NA-86/18
Stable boundary conditions for some hyperbolic difference schemes,
J D P Donnelly
NA-86/19
A version of moving finite elements for one-dimensional parabolic equations,
J D P Donnelly
NA-86/20
A multigrid pressure correction method for incompressible flows,
G J Shaw, S Sivaloganathan
NA-86/21
Convergence rates of difference schemes on weak solutions of the heat transfer equation,
M Drazic
NA-86/22
Finite difference methods for parabolic problems with nonsmooth initial data,
W L Seward, J A Scott
NA-86/23
Optimal recovery in the finite element method Part 1: Recovery from weighted L_{2} fits,
K W Morton, G Moore, J W Barrett
NA-87/1
A theoretical and practical smoothing analysis of the simple pressure-correction algorithm,
S Sivaloganathan, G J Shaw
NA-87/2
A constructive approach to the existence theory for the equation governing porous medium combustion,
A Stuart
NA-87/3
Symmetry-breaking in semilinear elliptic equations with critical growth rates,
J Norbury, C J Budd
NA-87/4
Convection dominated flows using Moores' upwinding method,
D J Benson
NA-87/5
Stability of implicit finite difference schemes for the solution of IBVP's,
S J Wardrop
NA-87/6
A finite volume scheme with shock fitting for the steady Euler equations,
M Paisley, K W Morton
NA-87/7
Studies in simple turbulence models,
J T Ratnanather
NA-87/8
Moving point and particle methods for convection-diffusion equations,
M D Rees
NA-87/9
Applications of Shilnikov theory to semilinear elliptic equations,
C J Budd
NA-87/10
Convergence properties of the Lagrange-Galerkin method with and without exact integration,
R O Jack
NA-87/11
Solutions of an elliptic boundary value problem with a discontinuous nonlinearity,
J G Kolibal
NA-87/12
Exact solutions of the space charge equation using the hodograph method,
A A Wheeler, C J Budd
NA-87/13
A new approach to the space charge problem,
A A Wheeler, C J Budd
NA-87/14
The existence of bounded solutions of a semi-linear heat equation,
Y W Qi
NA-87/15
Optimal recovery in the finite element method: Part 2: Recovery from ODE best fits by defect correction,
K W Morton, G Moore, J W Barrett
NA-88/1
Stability limits for Preissmann's scheme,
C P Skeels, P G Samuels
NA-88/2
Numerical solution of the heat equation on triangular grids,
M D Rees
NA-88/3
Symmetry breaking and semi-linear elliptic equations,
C J Budd
NA-88/4
Analysis of multigrid algorithms for solution of convection-dominated flows,
S A Trickett, D Mayers
NA-88/5
The cell vertex method for steady compressible flow,
M A Rudgyard, P N Childs, K W Morton
NA-88/6
A spectral method of characteristics for first-order hyperbolic equations,
A Ware, E Süli
NA-88/7
Characteristic Galerkin methods for hyperbolic systems,
P N Childs, K W Morton
NA-88/8
The study of a semilinear elliptic equation from a combustion problem,
Y W Qi
NA-88/9
Coronas and space charge phenomena,
A A Wheeler, C J Budd
NA-88/10
Analysis and Application of an efficient line solver based upon the Symmetrical Coupled Gauss-Seidel Scheme,
T M Shah, D F Mayers, J S Rollett
NA-88/11
Coronas and the space charge problem,
C J Budd
NA-88/12
A numerical scheme for the solution of the space charge problem on a multiply connected region,
A A Wheeler, C J Budd
NA-88/13
The convergence of B spline quasi interpolants in one and two dimensions,
P Gonzalez-Casanova
NA-88/14
The asymptotic behaviour of the solutions of the Kassoy problem with a modified source term,
Y W Qi, C J Budd
NA-88/15
Stability of the Lagrange-Galerkin method: the performance of quadrature in theory and practice,
R O Jack
NA-89/1
Moving point, particle and free Lagrange methods for convection-diffusion equations,
M D Rees, K W Morton
NA-89/2
Unsymmetric conjugate gradient methods and sparse direct methods in finite element flow simulation,
J S Rollett, W M Connolley, D Howard
NA-89/3
Roe's approximation for a two-phase slug flow model,
Xin Kai Li, J D P Donnelly
NA-89/4
The cell vertex method for viscous transport problem,
J Mackenzie
NA-89/5
Fitting data subject to weak continuity constraints,
J D P Donnelly
NA-89/6
Methods on distorted meshes -- stability, accuracy and adaptivity,
E Süli
NA-89/7
The finite element method with nodes for convection diffusion equations,
E Süli, Y Tourigny
NA-89/8
Finite element principles for evolutionary problems with applications to Oil Reservoir modelling,
A K Parrott, K W Morton
NA-89/9
The convergence of B spline quasi-interpolants in one and two dimensions Part II -- Non-regular grid,
P Gonzalez-Casanova
NA-89/10
Spectral Lagrange-Galerkin method for the Navier-Stokes equations: accuracy and nonlinear stability,
A Ware, E Süli
NA-89/11
Finite volume methods with explicit shock representation,
M Rudgyard, K W Morton
NA-89/12
A wave in two-phase flow model,
Xin Kai Li
NA-89/13
A semi-implicit method for two-phase flow problems,
Xin Kai Li
NA-90/1
Finite volume solutions of convection-diffusion test problems,
K W Morton, J A Mackenzie
NA-90/2
The numerical study of blow-up with application to a nonlinear Schrodinger equation,
J M Sanz-Serna, Y Tourigny
NA-90/3
A k-epsilon finite element method for an axi-symmetric jet confined in a diverging duct of circular section,
D Howard
NA-90/4
L_infty errors in finite volume approximations,
R Jones
NA-90/5
Upwind iteration methods for the cell-vertex scheme -- one dimensional problems,
M A Rudgyard
NA-90/6
Computing the shape of a flexible wire in three dimensions,
D C Handscomb
NA-90/7
Convergence of finite volume schemes for Poisson's equation on non-uniform meshes,
E Süli
NA-90/9
Approximation of the diffusion term in the method of moving finite elements,
J D P Donnelly
NA-90/10
An exact solution for moving finite elements applied to the viscous Burgers' equation,
J D P Donnelly
NA-90/11
Finite volume methods and their analysis,
K W Morton
NA-90/12
Cell vertex finite volume discretisations in three dimensions,
G J Shaw, P I Crumpton
NA-90/13
Lagrange-Galerkin and characteristic-Galerkin methods and their applications,
K W Morton
NA-90/14
Finite volume methods and their analysis,
E Süli, K W Morton
NA-90/15
Airfoil design via Jameson's optimal control approach,
C Yiu
NA-90/16
Stability of finite volume and finite element methods in discrete W^{2,0} norm,
R Jones
NA-90/17
Error estimates for adaptive methods,
R Jones
NA-90/18
Multiquadric error estimates in Sobolev spaces,
P Gonzalez-Casanova
NA-90/19
Implementation of a multigrid method on a transputer network,
A Stewart, G J Shaw
NA-90/20
A parallel multigrid FAS scheme for transputer networks,
A Stewart, G J Shaw
NA-90/21
Some novel results on Newton's method for matrix inversion,
P I Crumpton, G J Shaw
NA-90/22
Optimal error estimation for Petrov-Galerkin methods in two dimension,
E Süli, T Murdoch, K W Morton
NA-91/1
Intrinsic properties of cubic splines with equi-spaced knots,
J Zhao
NA-91/2
Numerical investigations of boundary layer effects in a shock tube,
K J Badcock
NA-91/4
Discretisation of a convection-diffusion equation,
K W Morton, I J Sobey
NA-91/5
Interpolation and differentiation of multivariate functions and interpolation of divergence-free vector fields using surface splines,
D C Handscomb
NA-91/6
A high order method for the solution of free boundary problems,
J D P Donnelly
NA-91/7
An analysis of the cell vertex method,
K W Morton, M J Stynes
NA-91/8
Euler Characteristic Galerkin scheme with recovery,
K W Morton, P Lin, E Süli
NA-91/9
Upwind iteration methods for the cell vertex scheme in one dimension,
K W Morton, M A Rudgyard, G J Shaw
NA-91/10
Pseudospectra of matrices,
L N Trefethen
NA-91/11
Upwinded test functions for finite element and finite volume methods,
K W Morton
NA-91/12
Cell vertex algorithms for the compressible Navier-Stokes equations,
P I Crumpton, J A Mackenzie, K W Morton
NA-91/13
Analysis of a supraconvergent cell vertex finite volume method for one-dimensional convection-diffusion problems,
B Garcia-Archilla, J A Mackenzie
NA-91/14
Design of a gas bearing,
W R Smith, D F Mayers, S O Howison
NA-91/16
Finite volume methods for modelling the Navier-Stokes equations,
K W Morton
NA-92/1
Characteristic Galerkin schemes for scalar conservation laws in two space dimensions I: Formulation,
P Lin, K W Morton, E Süli
NA-92/2
Non-oscillatory finite-element approximations of steady convection-diffusion problems,
A P Weir, A K Parrott
NA-92/3
Defect correction methods for systems of conservation laws,
G J Shaw, P I Crumpton
NA-92/4
Gauss point mass lumping schemes for Maxwell's equations,
G Cohen, P Monk
NA-92/5
A vertex centred finite volume method with shock detection,
P I Crumpton, G J Shaw
NA-92/6
On the stability of Poiseuille flow of a Bingham fluid,
I A Frigaard, S D Howison, I J Sobey
NA-92/7
The setting up and solution of the cell vertex equation,
M R Field
NA-92/8
Approximation of attractors in Banach space,
A T Hill
NA-92/9
The Lerat scheme as a fast solver for the cell-vertex equations,
I C Glover
NA-92/10
Error estimates and mesh adaption for a cell vertex finite volume scheme,
J A Mackenzie, D F Mayers, A J Mayfield
NA-92/11
A family of numerical boundary conditions for the shallow water equations,
J D P Donnelly
NA-92/12
Analysis of a finite volume approximation of ODEs with non-smooth coefficients,
I Becvarova
NA-92/13
Gradient recovery and superconvergence phenomena in linear finite elements,
M Woodgate
NA-92/14
Dependence on numerical algorithm of bifurcation structure for flow through a symmetric expansion,
Y Uchibori, I J Sobey
NA-92/15
Evolution-Galerkin methods and their supra-convergence,
K W Morton, E Süli
NA-92/16
Discretisation and multigrid solution of elliptic equations with strongly discontinuous coefficients,
G J Shaw, P I Crumpton
NA-92/17
A convergence analysis of Yee's scheme on non-uniform grids,
P Monk, E Süli
NA-92/18
Large time behaviour of solutions to the magneto-hydrodynamics equation,
M E Schonbek, T P Schonbek, E Süli
NA-92/19
Stability and convergence of the spectral Lagrange-Galerkin method for periodic/non-periodic convection-dominated diffusion problem,
M Baker, E Süli, A Ware
NA-92/20
A dispersion analysis of Finite Element Methods for Maxwell's equations,
A K Parrott, P Monk
NA-92/22
An example of instability phenomena in hyperbolic IBVP,
N A Burgess, K W Morton
NA-92/23
Tools for analysis of convergence of conjugate-gradient-type methods,
F F Campos filho, J S Rollett
NA-92/24
Study of convergence behaviour of conjugate-gradient-type methods for solving unsymmetric systems,
F F Campos filho, J S Rollett
NA-93/01
Some exact solutions in moving finite elements,
J D P Donnelly
NA-93/02
Lower bounds for the spectrum of non-selfadjoint second order elliptic operators,
A T Hill
NA-93/03
A multigrid solution of the complex Helmholtz equation,
K Brackenridge
NA-93/04
A method for solving the algebriac non-linear systems that arise in chemical equilibrium problems,
F F Campos filho, J S Rollett
NA-93/05
A posteriori and a priori error error analysis of finite volume methods,
K W Morton, E Süli
NA-93/06
Dynamics of a nonlinear convection-diffusion equation in multi-dimensional domains,
A T Hill, E Süli
NA-93/07
Analysis of free divergence finite element methods,
P Balland, D F Mayers
NA-93/08
Set convergence for discretizations of the attractor,
A T Hill, E Süli
NA-93/09
A cell vertex method for 3D Navier-Stokes solutions,
P I Crumpton
NA-93/10
An upwind finite element method for hyperbolic systems of conservation laws,
P Lin, K W Morton
NA-93/11
The use of partial orthogonalisation for solving large sparse linear systems,
F F Campos filho, J S Rollett
NA-93/12
Spurious entropy generation as a mesh quality indicator,
J G Andrews
NA-93/13
An improved artificial dissipation model for the cell-vertex finite volume method,
J A Mackenzie
NA-94/1
Analysis of the cell vertex finite volume method for hyperbolic problems with variable coefficients,
P Balland, E Süli
NA-94/2
Analysis of a Godunov-type scheme with front-tracking,
P Balland, D F Mayers
NA-94/3
The splitting formulation of multilevel methods and some applications,
A Borzì
NA-94/4
Multigrid solution of the singularly perturbed convection-diffusion equation,
K Brackenridge
NA-94/5
Analysis of the cell vertex finite volume method for the Cauchy-Riemann equations,
M Vanmaele, K W Morton, E Süli, A Borzì
NA-94/6
Analysis of a cell-vertex finite volume method for convection diffusion problems,
K W Morton, M Stynes, E Süli
NA-94/7 (in preparation)
A superconvergence analysis of an edge-based finite element method for Maxwell's equations on non-uniform meshes,
E Süli, J C Wood
NA-94/8
Multilevel solution of cell vertex Cauchy-Riemann Equations,
A Borzì, K W Morton, E Süli, M Vanmaele
NA-94/9
A dual graph-norm refinement indicator for finite volume approximations of the Euler equations,
T Sonar, E Süli
NA-94/10
Analysis of preconditioners for the Conjugate Gradient Method,
F F Campos filho, J S Rollett
NA-94/11
A diffusion process with boundary singularity solved using the Finite Element Method: calculation of the steady state and time dependent currents at disc electrodes,
J Galceran, D J Gavaghan, J S Rollett
NA-94/12
An abstract formulation of the concept of entropy,
J D P Donnelly