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arXiv 1707.02153math.NAcs.NA
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一种用于耦合体-表面问题的切割不连续伽辽金方法

A Cut Discontinuous Galerkin Method for Coupled Bulk-Surface Problems

Umeå University(乌默奥大学)

Andre Massing

AI总结:

本文提出一种切割不连续伽辽金方法,用于求解耦合体-表面扩散-反应方程,通过添加稳定化项保证方法稳定性和最优收敛性。

摘要:

我们开发了一种切割不连续伽辽金方法(cutDGM),用于求解嵌入到结构化非适应背景网格中的体域中的扩散-反应方程,同时耦合到体域边界的相应方程。通过在耦合体-表面问题的离散变分公式中添加特定的稳定化项,所得到的cutDGM被证明是稳定的,并通过数值实验展示了最优收敛性。我们还理论和数值证明了系统矩阵在体域相对于背景网格位置变化时仍保持良好条件数。

英文摘要:

We develop a cut Discontinuous Galerkin method (cutDGM) for a diffusion-reaction equation in a bulk domain which is coupled to a corresponding equation on the boundary of the bulk domain. The bulk domain is embedded into a structured, unfitted background mesh. By adding certain stabilization terms to the discrete variational formulation of the coupled bulk-surface problem, the resulting cutDGM is provably stable and exhibits optimal convergence properties as demon- strated by numerical experiments. We also show both theoretically and numerically that the system matrix is well-conditioned, irrespective of the relative position of the bulk domain in the background mesh.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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