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Adaptive finite elements for a linear parabolic problem. (English) Zbl 0935.65105

Summary: A posteriori error estimates for the heat equation in two space dimensions are presented. A classical discretization is used, Euler backward in time, and continuous, piecewise linear triangular finite elements in space. The error is bounded above and below by an explicit error estimator based on the residual. Numerical results are presented for uniform triangulations and constant time steps. The quality of our error estimator is discussed. An adaptive algorithm is then proposed. Successive Delaunay triangulations are generated, so that the estimated relative error is close to a present tolerance. Again, numerical results demonstrate the efficiency of our approach.

MSC:

65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs

Software:

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References:

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