论文标题
Lagrange乘数法的后验误差分析用于Stokes/Biot流体弹性结构相互作用模型
A posteriori error analysis for a Lagrange multiplier method for a Stokes/Biot fluid-poroelastic structure interaction model
论文作者
论文摘要
在这项工作中，我们开发了一种构型混合有限元方法的后验错误分析，用于求解在$ \ Mathbb {r}^d $，$ d $，$ d $，$ d $ d \ in \ in \ in \ in \ {2,3,3，3,3，3，3，3，3,3，$中，在同型网络上的自由流体和流体之间的相互作用中产生的耦合问题。该方法利用了Ilona Ambartsumyan等人提出的半污染配方。在（Numerische Mathematik，2017年10月）。 A后验误差估计基于对有限元解决方案残差的适当评估。事实证明，本文提供的后验错误估计既可靠又有效。可靠性证明可利用合适的辅助问题，所涉及的双线性形式满足的各种连续INF-SUP条件，Helmholtz分解以及ClémentInterpolant的局部近似特性。另一方面，逆不平等以及基于简单的泡沫和面对面功能的本地化技术是证明估算器效率的主要工具。最多可以进行较小的修改，我们的分析可以扩展到其他有限元子空间，从而得出稳定的盖尔金方案。
In this work we develop an a posteriori error analysis of a conforming mixed finite element method for solving the coupled problem arising in the interaction between a free fluid and a fluid in a poroelastic medium on isotropic meshes in $\mathbb{R}^d$, $d\in\{2,3\}$. The approach utilizes the semi-discrete formulation proposed by Ilona Ambartsumyan et al. in (Numerische Mathematik, October 2017). The a posteriori error estimate is based on a suitable evaluation on the residual of the finite element solution. It is proven that the a posteriori error estimate provided in this paper is both reliable and efficient. The proof of reliability makes use of suitable auxiliary problems, diverse continuous inf-sup conditions satisfied by the bilinear forms involved, Helmholtz decomposition, and local approximation properties of the Clément interpolant. On the other hand, inverse inequalities, and the localization technique based on simplexe-bubble and face-bubble functions are the main tools for proving the efficiency of the estimator. Up to minor modifications, our analysis can be extended to other finite element subspaces yielding a stable Galerkin scheme.
