论文标题
基于旋转的毛弹性的混合和多点有限元方法
Mixed and multipoint finite element methods for rotation-based poroelasticity
论文作者
论文摘要
这项工作提出了一种用于生物孔隙弹性方程的混合有限元方法，该方法采用了最低的raviart-thomas thomas有限元元素空间，用于固体位移和流体压力的分段常数。该方法基于线性化弹性作为加权矢量拉普拉斯问题的制定。通过将实体旋转和流体通量作为辅助变量引入，我们形成了生物系统的四场公式，该公式使用符合符合的混合有限元元素空间离散化。随后以局部杂交技术从系统中删除辅助变量，以获得多点旋转旋转混合有限元方法。四场和多点混合有限元方法的稳定性和收敛性以加权规范的形式显示，这还导致参数刺激性预处理。数值实验证实了理论结果。
This work proposes a mixed finite element method for the Biot poroelasticity equations that employs the lowest-order Raviart-Thomas finite element space for the solid displacement and piecewise constants for the fluid pressure. The method is based on the formulation of linearized elasticity as a weighted vector Laplace problem. By introducing the solid rotation and fluid flux as auxiliary variables, we form a four-field formulation of the Biot system, which is discretized using conforming mixed finite element spaces. The auxiliary variables are subsequently removed from the system in a local hybridization technique to obtain a multipoint rotation-flux mixed finite element method. Stability and convergence of the four-field and multipoint mixed finite element methods are shown in terms of weighted norms, which additionally leads to parameter-robust preconditioners. Numerical experiments confirm the theoretical results.
