论文标题
磁通量混合有限元法具有多点通量近似
Flux-mortar mixed finite element methods with multipoint flux approximation
论文作者
论文摘要
最近为一类无匹配网格上的一般域分解鞍点问题开发了通量 - 验证混合有限元方法。在这项工作中，我们使用多点通量近似作为亚域离散化开发了Darcy流的方法。亚域问题涉及解决阳性确定的以细胞为中心的压力系统。亚域界面上的正常通量是砂浆耦合变量，该变量起着拉格朗日乘数的作用，以施加弱连续性压力。我们提出了基于将方法重新阐述为具有正交规则的混合有限元方法的拟合性和错误分析。我们为所得代数系统的解决方案开发了一种非重叠的域分解算法，该算法将其减少到磁通量 - 验证范围问题以及有效的接口预处理器。提供了一系列数值实验，说明了该方法在一般网格上的性能，包括在复杂的多孔介质中流动的应用。
The flux-mortar mixed finite element method was recently developed for a general class of domain decomposition saddle point problems on non-matching grids. In this work we develop the method for Darcy flow using the multipoint flux approximation as the subdomain discretization. The subdomain problems involve solving positive definite cell-centered pressure systems. The normal flux on the subdomain interfaces is the mortar coupling variable, which plays the role of a Lagrange multiplier to impose weakly continuity of pressure. We present well-posedness and error analysis based on reformulating the method as a mixed finite element method with a quadrature rule. We develop a non-overlapping domain decomposition algorithm for the solution of the resulting algebraic system that reduces it to an interface problem for the flux-mortar, as well as an efficient interface preconditioner. A series of numerical experiments is presented illustrating the performance of the method on general grids, including applications to flow in complex porous media.
