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

Chris Budd; Othmar Koch; Leila Taghizadeh; Ewa Weinmüller

doi:10.1007/s10092-018-0286-z

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

Chris Budd, Othmar Koch, Leila Taghizadeh, Ewa Weinmüller

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1 Citation (SciVal)

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.

Original language	English
Article number	43
Journal	Calcolo
Volume	55
Issue number	4
DOIs	https://doi.org/10.1007/s10092-018-0286-z
Publication status	Published - 1 Dec 2018

Bibliographical note

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

Keywords

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

ASJC Scopus subject areas

Algebra and Number Theory
Computational Mathematics

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10.1007/s10092-018-0286-z

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title = "Asymptotic properties of the space–time adaptive numerical solution of a nonlinear heat equation",

abstract = "We consider the fully adaptive space–time discretization of a class of nonlinear heat equations by Rothe{\textquoteright}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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author = "Chris Budd and Othmar Koch and Leila Taghizadeh and Ewa Weinm{\"u}ller",

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AU - Budd, Chris

AU - Koch, Othmar

AU - Taghizadeh, Leila

AU - Weinmüller, Ewa

PY - 2018/12/1

Y1 - 2018/12/1

N2 - 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.

AB - 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.

KW - Adaptivity

KW - Backward Euler method

KW - Collocation methods

KW - Evolution equations

KW - Rothe’s method

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JO - Calcolo

JF - Calcolo

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ER -

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

Abstract

Bibliographical note

Keywords

ASJC Scopus subject areas

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