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2000

A posteriori error estimation and adaptivity for degenerate parabolic problems

8 years 7 months ago
A posteriori error estimation and adaptivity for degenerate parabolic problems
Abstract. Two explicit error representation formulas are derived for degenerate parabolic PDEs, which are based on evaluating a parabolic residual in negative norms. The resulting upper bounds are valid for any numerical method, and rely on regularity properties of solutions of a dual parabolic problem in nondivergence form with vanishing diffusion coefficient. They are applied to a practical space-time discretization consisting of C0 piecewise linear finite elements over highly graded unstructured meshes, and backward finite differences with varying time-steps. Two rigorous a posteriori error estimates are derived for this scheme, and used in designing an efficient adaptive algorithm, which equidistributes space and time discretization errors via refinement/coarsening. A simulation finally compares the behavior of the rigorous a posteriori error estimators with a heuristic approach, and hints at the potentials and reliability of the proposed method.
Ricardo H. Nochetto, Alfred Schmidt, C. Verdi
Added 19 Dec 2010
Updated 19 Dec 2010
Type Journal
Year 2000
Where MOC
Authors Ricardo H. Nochetto, Alfred Schmidt, C. Verdi
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