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Journal of Scientific Computing

Erschienen in:

01.03.2014

Optimal Error Analysis of Galerkin FEMs for Nonlinear Joule Heating Equations

verfasst von: Huadong Gao

Erschienen in: Journal of Scientific Computing | Ausgabe 3/2014

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Abstract

We study in this paper two linearized backward Euler schemes with Galerkin finite element approximations for the time-dependent nonlinear Joule heating equations. By introducing a time-discrete (elliptic) system as proposed in Li and Sun (Int J Numer Anal Model 10:622–633, 2013; SIAM J Numer Anal (to appear)), we split the error function as the temporal error function plus the spatial error function, and then we present unconditionally optimal error estimates of \(r\)th order Galerkin FEMs (\(1 \le r \le 3\)). Numerical results in two and three dimensional spaces are provided to confirm our theoretical analysis and show the unconditional stability (convergence) of the schemes.

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Titel: Optimal Error Analysis of Galerkin FEMs for Nonlinear Joule Heating Equations
verfasst von: Huadong Gao
Publikationsdatum: 01.03.2014
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 3/2014
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-013-9746-4

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