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arXiv · 1208.4698

Error analysis of linearized semi-implicit Galerkin finite element methods for nonlinear parabolic equations

Buyang Li·Weiwei Sun
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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 the error and precise analysis of a corresponding time-discrete system. The method used in this paper can be applied to 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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Buyang Li, Weiwei Sun. 2012-08-23. Error analysis of linearized semi-implicit Galerkin finite element methods for nonlinear parabolic equations. https://arxiv.org/abs/1208.4698

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