zbMATH — the first resource for mathematics

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

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