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A posteriori analysis of the finite element discretization of some parabolic equations. (English) Zbl 1072.65124

The authors present an analysis of a finite element method for the semilinear heat equation. The spatial discretization uses polynomnial finite elements on triangles or trapezoids, and the temporal discretization is by the backward Euler method. The authors present an a posteriori error bound based on an estimate of the global temporal variation and a local spatial estimate using the residual and the jumps in the flux.

MSC:

65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K55 Nonlinear parabolic equations
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