# 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