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

Buyang Li, Weiwei Sun
2013 arXiv   pre-print
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
more » ... ime-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 τ.
arXiv:1208.4698v6 fatcat:my4eugksizhorkl6kyev7fgtse