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01-12-2018

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

Authors: Chris Budd, Othmar Koch, Leila Taghizadeh, Ewa Weinmüller

Published in: Calcolo | Issue 4/2018

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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.

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Title: Asymptotic properties of the space–time adaptive numerical solution of a nonlinear heat equation
Authors: Chris Budd
Othmar Koch
Leila Taghizadeh
Ewa Weinmüller
Publication date: 01-12-2018
Publisher: Springer International Publishing
Published in: Calcolo / Issue 4/2018
Print ISSN: 0008-0624
Electronic ISSN: 1126-5434
DOI: https://doi.org/10.1007/s10092-018-0286-z

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

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