Error Analysis of Linearized Semi-Implicit Galerkin Finite Element Methods for Nonlinear Parabolic Equations
Year: 2013
International Journal of Numerical Analysis and Modeling, Vol. 10 (2013), Iss. 3 : pp. 622–633
Abstract
This paper is concerned with the time-step condition of commonly-used linearized semi-implicit schemes for nonlinear parabolic PDEs with Galerkin finite element approximations. In particular, we study the time-dependent nonlinear Joule heating equations. We present optimal error estimates of the semi-implicit Euler scheme in both the $L^2$ norm and the $H^1$ norm without any time-step restriction. Theoretical analysis is based on a new splitting of error function and precise analysis of a corresponding time-discrete system. The method used in this paper is applicable for more general nonlinear parabolic systems and many other linearized (semi)-implicit time discretizations for which previous works often require certain restriction on the time-step size $\tau$.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2013-IJNAM-586
International Journal of Numerical Analysis and Modeling, Vol. 10 (2013), Iss. 3 : pp. 622–633
Published online: 2013-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 12
Keywords: Nonlinear parabolic system unconditionally optimal error estimate linearized semi-implicit scheme Galerkin method.