deal.II implementation of a weak Galerkin finite element solver for Darcy flow
deal.II implementation of a weak Galerkin finite element solver for Darcy flow
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deal.II 达西流弱伽辽金有限元求解器的实现
DOI：
10.1007/978-3-030-22747-0_37
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
Tavener, Simon
中科院分区：
文献类型：
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作者：
Wang, Zhuoran;Harper, Graham;O'Leary, Patrick;Liu, Jiangguo;Tavener, Simon
提出了一种求解达西流的弱Galerkin （WG）有限元求解器，并在deal. i平台上进行了实现。求解器可以统一地求解四边形和六面体网格。它通过在元素内部和边/面分别定义的q型次多项式近似压力。基于离散弱梯度的新概念，通过后处理在未映射的Raviart-Thomas空间中获得数值速度。求解器是局部质量保守的，并产生连续的法向通量。实现不理想。它允许多项式次数最多为5。数值实验表明，本文提出的求解方法优于传统的混合有限元方法。
This paper presents a weak Galerkin (WG) finite element solver for Darcy flow and its implementation on thedeal.IIplatform. The solver works for quadrilateral and hexahedral meshes in a unified way. It approximates pressure byQ-type degreepolynomials separately defined in element interiors and on edges/faces. Numerical velocity is obtained in the unmapped Raviart-Thomas spacevia postprocessing based on the novel concepts of discrete weak gradients. The solver is locally mass-conservative and produces continuous normal fluxes. The implementation indeal.IIallows polynomial degrees up to 5. Numerical experiments show that our new WG solver performs better than the classical mixed finite element methods.