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, 55:43 | Cite as

Asymptotic properties of the space–time adaptive numerical solution of a nonlinear heat equation

  • Chris Budd
  • Othmar Koch
  • Leila Taghizadeh
  • Ewa Weinmüller
Article
  • 71 Downloads

Abstract

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.

Keywords

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

Mathematics Subject Classification

65M20 65L05 65L10 65L50 

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Copyright information

© Istituto di Informatica e Telematica del Consiglio Nazionale delle Ricerche 2018

Authors and Affiliations

  1. 1.Mathematical SciencesUniversity of BathBathUK
  2. 2.Institut für MathematikUniversität WienViennaAustria
  3. 3.Institut für Analysis und Scientific ComputingTechnische Universität WienViennaAustria

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