论文标题
不匹配网格上的通量摩尔塔尔混合有限元方法
Flux-mortar mixed finite element methods on non-matching grids
论文作者
论文摘要
我们研究了一种在不匹配的网格上选择正常通量作为耦合变量的非匹配网格上的混合有限元近似值的砂浆技术。它扮演着拉格朗日乘数的角色，以施加弱连续性压力。在问题的混合配方中，正常通量是必不可少的边界条件，并与使用合适的扩展运算符合并。考虑了两个这样的扩展运算符，我们分析了所得制剂，方面的稳定性和收敛性。我们进一步概括了理论结果，表明相同的域分解技术适用于满足轻度假设的一类鞍点问题。提出了耦合的stokes-darcy流的示例。
We investigate a mortar technique for mixed finite element approximations of Darcy flow on non-matching grids in which the normal flux is chosen as the coupling variable. It plays the role of a Lagrange multiplier to impose weakly continuity of pressure. In the mixed formulation of the problem, the normal flux is an essential boundary condition and it is incorporated with the use of suitable extension operators. Two such extension operators are considered and we analyze the resulting formulations with respect to stability and convergence. We further generalize the theoretical results, showing that the same domain decomposition technique is applicable to a class of saddle point problems satisfying mild assumptions. An example of coupled Stokes-Darcy flows is presented.
