弱Galerkin有限元法的稳定性

Stability of Weak Galerkin Finite Element Method

考虑求解二阶椭圆方程和Biharmonic方程的弱Galerkin有限元方法的稳定性.首先,在弱Galerkin有限元法中引入弱函数和弱梯度算子来近似标准函数和标准梯度算子;其次,给出弱函数空间下范数·和·-1的定义,基于这两种范数得到了弱Galerkin有限元方法的稳定性.

We considered the stability of the weakGalerkin finite element method for solving the second order elliptic equations and Biharmonic equations.Firstly,we introduced the weak functions and the weak gradient operators to approximate the standard functions and standard differentialoperators in the weak Galerkin method.Secondly,we gave the definitions of normsof·and·-1in the weak function space,and obtained the stability of the weak Galerkin finite element method based on the two norms.