Prof. Wei-Wei Sun Department of Mathematics, City University of Hong Kong E-mail: maweiw@math.cityu.edu.hk

Abstract: Linearized (semi)-implicit schemes are the most commonly-used approximations in numerical solution of nonlinear parabolic equations since at each time step, the schemes only require the solution of a linear system. However time step restriction condition of schemes is always a key issue in analysis and computation. For many nonlinear parabolic systems, error analysis of Galerkin finite element methods (or finite difference method) with linearized semi-implicit schemes in the time direction often requires certain time step conditions, Such time-step restrictions may result in the use of a very small time step and extremely time-consuming in practical computations. In this talk, we introduce a new approach to unconditional error analysis of linearized semi-implicit Galerkin FEMs for a large class of nonlinear parabolic PDEs.