Superconvergence of mixed finite element semi-discretizations of two time-dependent problems. (English) Zbl 1059.65518

The aim of the paper is to extend some superconvergence results for elliptic problems to time dependent problems. Two-dimensional space variables are discretized by a mixed finite element method whereas time remains continuous. Superconvergence error estimates are derived for a diffusion problem. The author also generalizes P. Monk’s results for lower order finite element approximation of the Maxwell equations to higher order elements. The obtained order of superconvergence for semidiscrete time dependent schemes is the same as for time independent problems.


65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
78M10 Finite element, Galerkin and related methods applied to problems in optics and electromagnetic theory
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