Wang Feng, Cai Mingchao, Wang Gang, Zeng Yuping
Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China.
Department of Mathematics, Morgan State University, Baltimore, MD 21251, USA.
Comput Math Appl. 2022 Nov 15;126:31-42. doi: 10.1016/j.camwa.2022.09.005. Epub 2022 Sep 16.
In this paper, we shall present a weak virtual element method for the standard three field poroelasticity problem on polytopal meshes. The flux velocity and pressure are approximated by the low order virtual element and the piecewise constant, while the elastic displacement is discretized by the virtual element with some tangential polynomials on element boundaries. A fully discrete scheme is then given by choosing the backward Euler for the time discretization. With some assumptions on the exact solutions, we prove that the convergence order is of order 1 with respect to the meshsize and the time step, and the hidden constants are independent of the parameters of the problems. Some numerical experiments are given to verify the results.
在本文中，我们将针对多面体网格上的标准三场多孔弹性问题提出一种弱虚拟单元法。通量速度和压力分别由低阶虚拟单元和分段常数近似，而弹性位移则通过在单元边界上具有一些切向多项式的虚拟单元进行离散化。然后通过选择向后欧拉方法进行时间离散化，给出一个全离散格式。在对精确解做出一些假设的情况下，我们证明了关于网格尺寸和时间步长，收敛阶为1，并且隐藏常数与问题的参数无关。给出了一些数值实验来验证结果。
