A Finite Element Method Based on Weighted Interior Penalties for Heterogeneous Incompressible Flows
A Finite Element Method Based on Weighted Interior Penalties for Heterogeneous Incompressible Flows
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DOI：
10.1137/080726318
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发表时间：
2009-10
期刊：
影响因子：
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通讯作者：
C. D'Angelo;P. Zunino
中科院分区：
文献类型：
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作者：
C. D'Angelo;P. Zunino
我们提出了一个有限元方案，用于近似线性不可压缩流（例如，Stokes' and Darcy's equations）。我们利用稳定的混合有限元与Nitsch型匹配条件，自动适应不同的子问题组合的耦合。最优误差估计的耦合问题。然后，我们提出并分析了一种通过一系列独立和局部子问题逼近多域解的迭代分裂策略。由于引入了一个合适的松弛策略，迭代方法原来是收敛的任何可能的子问题之间的耦合。
We propose a finite element scheme for the approximation of multidomain heterogeneous problems arising in the general framework of linear incompressible flows (e.g., Stokes' and Darcy's equations). We exploit stabilized mixed finite elements together with Nitsche-type matching conditions that automatically adapt to the coupling of different subproblem combinations. Optimal error estimates are derived for the coupled problem. Then, we propose and analyze an iterative splitting strategy for the approximation of the multidomain solution by means of a sequence of independent and local subproblems. Thanks to the introduction of a suitable relaxation strategy, the iterative method turns out to be convergent for any possible coupling between subproblems.