Error analysis of linearized semi-implicit Galerkin finite element methods for nonlinear parabolic equations (Q2865632)

The paper studies the time-step condition of commonly-used linearized semi-implicit schemes for nonlinear parabolic partial differential equations with Galerkin finite element approximations. The authors study the time-dependent nonlinear Joule heating equations. The paper presents 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. The method used is applicable for more general nonlinear parabolic systems and many other linearized (semi-) implicit time discretizations.