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Analysis of the Element-Free Galerkin Method with Penalty for Stokes Problems
1School of Mathematics, Physics and Data Science, Chongqing University of Science & Technology, Chongqing 401331, China.
Abstract:
The element-free Galerkin (EFG) method with penalty for Stokes problems is proposed and analyzed in this work. A priori error estimates of the penalty method, which is used to deal with Dirichlet boundary conditions, are derived to illustrate its validity in a continuous sense. Based on a feasible assumption, it is proved that there is a unique weak solution in the modified weak form of penalized Stokes problems. Then, the error bounds with the penalty factor for the EFG discretization are derived, which provide a rationale for choosing an efficient penalty factor. Numerical examples are given to confirm the theoretical results.
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