Numerical solution of semilinear integrodifferential equations of parabolic type with nonsmooth data. (English) Zbl 0701.65091

Le Roux, Marie-Noëlle; Thomée, Vidar

SIAM J. Numer. Anal. 26, No. 6, 1291-1309 (1989).

The integrodifferential equation \(u_ t+Au=B(u)\) with elliptic second- order operator A and with nonlinear integral operator \(B(u)=\int^{t}_{0}f(t,s,x,u(x,s))ds\) is studied. For the numerical solution by the Galerkin finite element method approximation properties are derived. Error estimates are derived for the discretization, in space by finite elements and in time variable by the backward Euler method, of a parabolic equation with a semilinear memory term. Special attention is paid to the case of nonsmooth data and to the computation of the memory term by quadrature.

Reviewer: S.Mika

MSC:

65R20	Numerical methods for integral equations
45J05	Integro-ordinary differential equations
45G10	Other nonlinear integral equations

Keywords:

integrodifferential equation; nonlinear integral operator; Galerkin finite element method; Error estimates; backward Euler method; semilinear memory term; nonsmooth data