On the Galerkin finite element approximations to multi-dimensional differential and integro-differential parabolic equations
The semidiscretization of differential and integro-differential equations of parabolic type with up to three spatial dimensions by means of a Galerkin finite element method is considered. The author proves error estimates in the maximum norm by using the operator method. These estimates are of optimal or almost optimal order in the case of simplicial Lagrangian polynomial elements. With the paper in hand, earlier results that provide error analysis in the \(L_2\)-norm or for the case of a time-independent elliptic operator are extended.
scientific article; zbMATH DE number 1033759
scientific article