C. Budd, O. Koch, L. Taghizadeh, E. Weinmüller:
"Asymptotic properties of the space-time adaptive numerical solution of a nonlinear heat equation";
Calcolo, 55 (2018), 43; 14 S.

Kurzfassung englisch:
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 equi-distribution 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.

Evolution equations Rothe´s method Collocation methods Backward Euler method Adaptivity

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