Lars B. Wahlbin

Optimal _{∞} error estimates for Galerkin approximations to solutions of two-point boundary value problems

A priori error estimates in the maximum norm are derived for Galerkin approximations to solutions of two-point boundary valud problems. The class of Galerkin spaces considered includes almost all (quasiuniform) piecewise-polynomial spaces that are used in practice. The estimates are optimal in the sense that no better rate of approximation is possible in general in the spaces employed.

Ritz-Volterra projections to finite-element spaces and applications to integrodifferential and related equations

The object of this paper is to investigate the convergence of finite-element approximations to solutions of parabolic and hyperbolic integrodifferential equations, and also of equations of Sobolev and viscoelasticity type. The concept of Ritz–Volterra projection will be seen to unify much of the analysis for the different types of problems. Optimal order error estimates are obtained in

Some Convergence Estimates for Semidiscrete Galerkin Type Approximations for Parabolic Equations

L_p

Besov spaces and applications to difference methods for initial value problems

for

Numerical solution of parabolic integro-differential equations by the discontinuous Galerkin method

2 \leqq p < \infty

Finite element approximation of a parabolic integro-differential equation with a weakly singular kernel

, and almost optimal order pointwise results given.

On Galerkin Methods in Semilinear Parabolic Problems

In this paper we derive convergence estimates for certain semidiscrete methods used in the approximation of solutions of initial boundary value problems with homogeneous Dirichlet boundary conditions for parabolic equations. These methods contain the ordinary Galerkin method based on approximating subspaces with functions vanishing on the boundary of the basic domain, and also some methods without such restrictions. The results include

On the sharpness of certain local estimates for ¹ projections into finite element spaces: influence of a re-entrant corner

L_2

Error estimates for a Galerkin method for a class of model equations for long waves

estimates, maximum norm estimates, interior estimates for difference quotients and superconvergence estimates. Some proofs depend on known results for the associated elliptic problem. Several of these estimates are derived for positive time under weak assumptions on the initial data.

Long-time numerical solution of a parabolic equation with memory

Fourier multipliers on Lp.- Besov spaces.- Initial value problems and difference operators.- The heat equation.- First order hyperbolic equations.- The Schrodinger equation.