论文标题
线性毛线弹性问题的弱甘针有限元法
Weak Galerkin finite element method for linear poroelasticity problems
论文作者
论文摘要
本文用于用于线性毛线弹性问题的弱伽勒金（WG）有限元方法，在这些问题中，引入了较弱定义的差异和梯度运算符在不连续函数方面。我们同时建立了连续的和离散的时间WG方案，并以离散的$ H^1 $规范获得其最佳收敛顺序估计，并在$ H^1 $类型中获得压力的$ H^1 $类型和$ l^2 $规范。最后，提出了数值实验，以说明理论误差以不同种类的网格结果显示，以显示网格选择的WG灵活性，并验证我们提出的方法的无锁定属性。
This paper is devoted to a weak Galerkin (WG) finite element method for linear poroelasticity problems where weakly defined divergence and gradient operators over discontinuous functions are introduced. We establish both the continuous and discrete time WG schemes, and obtain their optimal convergence order estimates in a discrete $H^1$ norm for the displacement and in an $H^1$ type and $L^2$ norms for the pressure. Finally, numerical experiments are presented to illustrate the theoretical error results in different kinds of meshes which shows the WG flexibility for mesh selections, and to verify the locking-free property of our proposed method.
