A DG Method for the Stokes Equations on Tensor Product Meshes with[Pk]d-Pk-1 Element

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外文摘要：We consider the mixed discontinuous Galerkin(DG)finite element approximation of the Stokes equation and provide the analysis for the[Pk]d-Pk-1 element on the tensor product meshes.Comparing to the previous stability proof with[Qk]d-Qk-1 discontinuous finite elements in the existing references,our first contribution is to extend the formal proof to the[Pk]d-Pk-1 discontinuous elements on the tensor product meshes.Numerical inf-sup tests have been performed to compare Qk and Pk types of elements and validate the well-posedness in both settings.Secondly,our contribution is to design the enhanced pressure-robust discretization by only modifying the body source assembling on[Pk]d-Pk-1 schemes to improve the numerical simulation further.The produced numerical velocity solution via our enhancement shows viscosity and pressure independence and thus outperforms the solution produced by standard discontinuous Galerkin schemes.Robustness analysis and numerical tests have been provided to validate the scheme's robustness.

外文关键词：

Finite elementDiscontinuous Galerkin(DG)methodTensor product meshEnhancement of pressure-robustness

作者：

Lin Mu、Xiu Ye、Shangyou Zhang、Peng Zhu

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作者单位：

Department of Mathematics,University of Georgia,Athens 30602,GA,USA

Department of Mathematics,University of Arkansas at Little Rock,Little Rock 72204,AR,USA

Department of Mathematical Sciences,University of Delaware,Newark 19716,DE,USA

College of Data Science,Jiaxing University,Jiaxing 314001,Zhejiang,China

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出版年：

2024

DOI：

10.1007/s42967-022-00243-9

应用数学与计算数学学报

上海大学

应用数学与计算数学学报

影响因子：0.165

ISSN：1006-6330

年,卷(期)：2024.6(4)