勷勤数学•专家报告

题      目：A pressure-robust numerical scheme for the Stokes equations based on the WOPSIP DG approach

报  告  人：曾玉平  教授  (邀请人：钟柳强)

                                    嘉应学院

时      间：11月29日  11：00-12：00

地     点：数科院西楼二楼会议室

报告人简介:

       曾玉平，博士，嘉应学院数学学院教授，从事有限元方法及其应用研究，主要致力于研究间断Galerkin，弱Galerkin，虚拟元等方法的先验和后验误差估计及其在流体力学中的应用，主持国家自然科学基金1项、广东省自然科学基金3项。在Journal of Scientific Computing, Journal of Computational Mathematics等计算数学期刊发表论文20多篇。

摘      要：

       We propose and analyze a new weakly over-penalized symmetric interior penalty (WOPSIP) discontinuous Galerkin (DG) scheme for the Stokes equations. The primary approach involves modifying the right-hand term and replacing the pressure-velocity coupling term $c_h(\cdot,\cdot)$ by incorporating a weak divergence instead of the divergence operator. These modifications allow for pressure-robustness in the scheme. We establish optimal order error estimates for the velocity $\boldsymbol{u}_h$ in discrete energy norm and $\boldsymbol{L}^2$ norm, as well as for the pressure $p_h$ in $L^2$ norm. We also provide numerical results to validate the effectiveness of the proposed scheme.

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