论文期刊

Discontinuous Galerkin methods of the Stokes equations with nonlinear damping term on general meshes




作者: Yongchao Zhang, Yanxia Qian, Liquan Mei
发表/完成日期: 2020-04-15
期刊名称: Computers and Mathematics with Applications
期卷: 79(8)
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论文简介
This paper presents the interior penalty discontinuous Galerkin (IPDG) methods to solve the stationary Stokes equations with nonlinear damping term. The IPDG discrete schemes are established on general meshes. The corresponding consistency and stabilization of those schemes are proved. Subsequently, we analyze the existence, boundedness and uniqueness of the discrete solutions. Then the optimal error estimates are derived in the L2-norm and H1-like DG-norm for the velocity variable and L2-norm for the pressure variable, respectively. Finally, some numerical experiments in two dimensional are reported to demonstrate the theoretical results and show the robustness of our discrete schemes.
https://doi.org/10.1016/j.camwa.2019.10.027