Extended Galerkin Method
Jinchao Xu, Penn State University
Sala conferenze IMATI-CNR, Pavia – Mercoledì 8 Maggio 2019 h.15:00
Abstract. In this talk, I will present a general framework, known as extended Galerkin method, for the derivation and analysis of many different types of finite element methods (including various discontinuous Galerkin methods).
For second order elliptic equation, this framework employs 4 different discretization variables, $u_h, p_h, \hat u_h$ and $\hat p_h$, where $u_h$ and $p_h$ are for approximation of $u$ and $p=\grad u$ inside each element, and $\hat u_h$ and $\hat p_h$ are for approximation of $u$ and $p\cdot n$ on the boundary of each element. The resulting 4-field discretization is proved to satisfy inf-sup conditions that are uniform with respect to all discretization and penalization parameters. As a result, most existing finite element and discontinuous Galerkin methods can be derived and analyzed using this general theory by making appropriate choices of discretization spaces and penalization parameters.