Asymptotic properties of the space–time adaptive numerical solution of a nonlinear heat equation
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We consider the fully adaptive space–time discretization of a class of nonlinear heat equations by Rothe’s method. Space discretization is based on adaptive polynomial collocation which relies on equidistribution of the defect of the numerical solution, and the time propagation is realized by an adaptive backward Euler scheme. From the known scaling laws, we infer theoretically the optimal grids implying error equidistribution, and verify that our adaptive procedure closely approaches these optimal grids.
KeywordsEvolution equations Rothe’s method Collocation methods Backward Euler method Adaptivity
Mathematics Subject Classification65M20 65L05 65L10 65L50