标题： 完全混合虚拟元法求解Biot问题 显示英文标题

标题： Fully-Mixed Virtual Element Method for the Biot Problem

摘要： 孔弹性力学描述了饱和多孔介质中变形与流体流动的相互作用。Biot孔弹性问题的一个全混合公式具有优势，能够更好地逼近达西速度和应力场，并满足局部质量和动量守恒。在这项工作中，我们专注于一种新的四场虚拟单元离散化方法来求解Biot方程。在定义离散空间时，强加了应力对称性，从而避免使用额外的拉格朗日乘子。完整的先验分析表明，所提出的数值方法对于极限材料属性具有鲁棒性。通过耦合空间近似与向后欧拉时间推进方案得到的最低阶全离散数值方法的一阶收敛性，由完整的三维数值验证得到了证实。还考虑了一个著名的孔弹性力学基准问题，以评估该方法的鲁棒性和计算性能。 显示英文摘要

摘要： Poroelasticity describes the interaction of deformation and fluid flow in saturated porous media. A fully-mixed formulation of Biot's poroelasticity problem has the advantage of producing a better approximation of the Darcy velocity and stress field, as well as satisfying local mass and momentum conservation. In this work, we focus on a novel four-fields Virtual Element discretization of Biot's equations. The stress symmetry is strongly imposed in the definition of the discrete space, thus avoiding the use of an additional Lagrange multiplier. A complete a priori analysis is performed, showing the robustness of the proposed numerical method with respect to limiting material properties. The first order convergence of the lowest-order fully-discrete numerical method, which is obtained by coupling the spatial approximation with the backward Euler time-advancing scheme, is confirmed by a complete 3D numerical validation. A well known poroelasticity benchmark is also considered to assess the robustness properties and computational performance.