Penalty-Free Any-Order Weak Galerkin FEMs for Elliptic Problems on Quadrilateral Meshes
Penalty-Free Any-Order Weak Galerkin FEMs for Elliptic Problems on Quadrilateral Meshes
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DOI：
10.1007/s10915-020-01239-4
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发表时间：
2020-06
影响因子：
2.5
通讯作者：
Jiangguo Liu;S. Tavener;Zhuoran Wang
中科院分区：
文献类型：
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作者：
Jiangguo Liu;S. Tavener;Zhuoran Wang
本文给出了求解凸四边形网格上椭圆边值问题的一类弱伽辽金有限元方法。这些新方法分别在单元内部和边缘上使用次多项式来逼近原始变量。在局部arbogast - coraspaces中建立了这些形状函数的离散弱梯度。然后用这些离散的弱梯度近似变分公式中的经典梯度。这些新方法不使用任何非物理惩罚因子，而是对原始变量、通量、法向通量和通量散度产生最优阶逼近。此外，这些新的求解器是局部保守的，并提供连续的正常通量。数值实验证明了这类新方法的准确性。
This paper presents a family of weak Galerkin finite element methods for elliptic boundary value problems on convex quadrilateral meshes. These new methods use degreepolynomials separately in element interiors and on edges for approximating the primal variable. The discrete weak gradients of these shape functions are established in the local Arbogast–Correaspaces. These discrete weak gradients are then used to approximate the classical gradient in the variational formulation. These new methods do not use any nonphysical penalty factor but produce optimal-order approximation to the primal variable, flux, normal flux, and divergence of flux. Moreover, these new solvers are locally conservative and offer continuous normal fluxes. Numerical experiments are presented to demonstrate the accuracy of this family of new methods.