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New Analysis on Galerkin FEMs for Nonlinear Parabolic PDEs

Banff International Research Station for Mathematical Innovation and Discovery

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 the time step restriction condition of schemes is always a key issue in analysis and computation. For many nonlinear parabolic systems, error analysis of Galerkin type finite element methods with linearized semi-implicit schemes in the time direction is established usually under certain time step condition $\tau \le h^{\alpha}$ for some $\alpha>0$. Such a time-step condition may result in the use of a very small time step and extremely time-consuming in practical computations. The problem becomes more serious when a non-uniform mesh or adaptive meshing is used. 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.

Mathematics; Numerical analysis; Partial differential equations

video/mp4

Author affiliation: City University of Hong Kong

2019-03-26

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/69230

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/