an:04149516
Zbl 0701.65091
Le Roux, Marie-No??lle; Thom??e, Vidar
Numerical solution of semilinear integrodifferential equations of parabolic type with nonsmooth data
EN
SIAM J. Numer. Anal. 26, No. 6, 1291-1309 (1989).
00155291
1989
j
65R20 45J05 45G10
integrodifferential equation; nonlinear integral operator; Galerkin finite element method; Error estimates; backward Euler method; semilinear memory term; nonsmooth data
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.
S.Mika