Analysis of a 2-field finite element solver for poroelasticity on quadrilateral meshes
Analysis of a 2-field finite element solver for poroelasticity on quadrilateral meshes
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DOI：
10.1016/j.cam.2021.113539
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发表时间：
2021-03
期刊：
影响因子：
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通讯作者：
Zhuoran Wang;S. Tavener;Jiangguo Liu
中科院分区：
文献类型：
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作者：
Zhuoran Wang;S. Tavener;Jiangguo Liu
本文提出了一种新的凸四边形网格上线性孔隙弹性问题的二维有限元解法。达西流离散流体压力的最低阶弱伽辽金（WG）有限元方法，建立离散的弱梯度和数值速度在最低阶Arbogast-Correa空间。线弹性离散固体位移的丰富拉格朗日有限元与特殊处理的体积膨胀。这两种类型的有限元耦合通过隐式欧拉时间离散求解孔隙弹性问题。一个严格的误差分析沿着与数值试验，以证明这种新的求解器的准确性和锁定的自由财产。
This paper presents a novel 2-field finite element solver for linear poroelasticity on convex quadrilateral meshes. The Darcy flow is discretized for fluid pressure by a lowest-order weak Galerkin (WG) finite element method, which establishes the discrete weak gradient and numerical velocity in the lowest-order Arbogast–Correa space. The linear elasticity is discretized for solid displacement by the enriched Lagrangian finite elements with a special treatment for the volumetric dilation. These two types of finite elements are coupled through the implicit Euler temporal discretization to solve poroelasticity problems. A rigorous error analysis is presented along with numerical tests to demonstrate the accuracy and locking-free property of this new solver.