Penalty-Free Any-Order Weak Galerkin FEMs for Linear Elasticity on Quadrilateral Meshes
Penalty-Free Any-Order Weak Galerkin FEMs for Linear Elasticity on Quadrilateral Meshes
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DOI：
10.1007/s10915-023-02151-3
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发表时间：
2023-02
影响因子：
2.5
通讯作者：
Ruishu Wang;Zhuoran Wang;Jiangguo Liu
中科院分区：
文献类型：
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作者：
Ruishu Wang;Zhuoran Wang;Jiangguo Liu
本文发展了一类新的弱伽辽金（WG）有限元方法，用于求解原始形式下的线性弹性问题。对于凸四边形网格，在单元内部和边缘分别使用度向量值多项式来逼近位移。这些新方法不需要惩罚或稳定剂。该方法没有泊松锁定，并且在位移、应力和位移散度方面具有最优的有序收敛率。在常用的测试用例上进行了数值实验，以说明这些新求解器的理论估计和有效性。简要讨论了对六面立方网格的推广。
This paper develops a family of new weak Galerkin (WG) finite element methods (FEMs) for solving linear elasticity in the primal formulation. For a convex quadrilateral mesh, degreevector-valued polynomials are used independently in element interiors and on edges for approximating the displacement. No penalty or stabilizer is needed for these new methods. The methods are free of Poisson-locking and have optimal orderconvergence rates in displacement, stress, and dilation (divergence of displacement). Numerical experiments on popular test cases are presented to illustrate the theoretical estimates and demonstrate efficiency of these new solvers. Extension to cuboidal hexahedral meshes is briefly discussed.