Vidar Thomée

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

ON RATIONAL APPROXIMATIONS OF SEMIGROUPS

L_p

Some Convergence Estimates for Semidiscrete Galerkin Type Approximations for Parabolic Equations

for

Besov spaces and applications to difference methods for initial value problems

2 \leqq p < \infty

Numerical solution of an evolution equation with a positive-type memory term

, and almost optimal order pointwise results given.

Time discretization of an integro-differential equation of parabolic type

We show that if

Nonsmooth data error estimates for approximations of an evolution equation with a positive-type memory term

r^n (hA),nh = t

The stability of rational approximations of analytic semigroups

, is an A-acceptable rational approximation of a strongly continuous semigroup

Superconvergence of a finite element approximation to the solution of a Sobolev equation in a single space variable

e^{tA}

Convergence Estimates for Galerkin Methods for Variable Coefficient Initial Value Problems

on a Banach space, then for t bounded,