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.

Original languageEnglish
Article number43
Issue number4
Publication statusPublished - 1 Dec 2018

Bibliographical note

Publisher Copyright:
© 2018, Istituto di Informatica e Telematica del Consiglio Nazionale delle Ricerche.


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

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Computational Mathematics


Dive into the research topics of 'Asymptotic properties of the space–time adaptive numerical solution of a nonlinear heat equation'. Together they form a unique fingerprint.

Cite this