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基于拉格朗日乘子的非协调嵌入式有限元方法的守恒性质

Conservation properties of non-conforming embedded finite-element methods based on lagrange multipliers.

作者信息

Nestola Maria Giuseppina Chiara, Zulian Patrick, Favino Marco, Krause Rolf

机构信息

Euler institute, Faculty of Informatics, Via La Santa 1, Viganello, 6962 Switzerland.

Faculty of Mathematics and Computer Science, UniDistance Suisse, Brig-Glis, 3900 Switzerland.

出版信息

BIT Numer Math. 2025;65(3):34. doi: 10.1007/s10543-025-01075-8. Epub 2025 Jul 18.

DOI:10.1007/s10543-025-01075-8
PMID:40689014
原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC12274252/
Abstract

Numerical simulations of Darcy flow in fractured porous media rely on hybrid- or equi-dimensional fracture models. The former considers fractures as lower-dimensional manifolds, while the latter treats them as objects of the same geometrical dimension as the porous matrix. Embedded strategies remove the inherent difficulties in mesh generation for fractured media, as they employ two different non-conforming meshes. While the Continuous Galerkin discretization has been shown to be locally conservative, this property has yet to be investigated for embedded strategies. This paper demonstrates that embedded strategies, based on dual Lagrange multiplier and discretized within a Continuous Galerkin framework, are locally conservative. We conduct a numerical analysis of the conservation properties in both hybrid- and equi-dimensional models for fractured porous media. Our results strongly support the conservation properties of embedded strategies.

摘要

裂隙多孔介质中达西流的数值模拟依赖于混合或等维裂隙模型。前者将裂隙视为低维流形，而后者将它们视为与多孔基质具有相同几何维度的对象。嵌入式策略消除了裂隙介质网格生成中固有的困难，因为它们采用了两种不同的非协调网格。虽然连续伽辽金离散化已被证明是局部守恒的，但对于嵌入式策略，这一特性尚未得到研究。本文证明了基于对偶拉格朗日乘子并在连续伽辽金框架内离散化的嵌入式策略是局部守恒的。我们对裂隙多孔介质的混合和等维模型中的守恒特性进行了数值分析。我们的结果有力地支持了嵌入式策略的守恒特性。

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本文引用的文献

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Large scale simulation of pressure induced phase-field fracture propagation using Utopia.使用乌托邦软件对压力诱导相场断裂扩展进行大规模模拟。
CCF Trans High Perform Comput. 2021;3(4):407-426. doi: 10.1007/s42514-021-00069-6. Epub 2021 Jun 29.
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A cut finite element method for elliptic bulk problems with embedded surfaces.一种用于具有嵌入表面的椭圆体问题的切割有限元方法。
GEM. 2019;10(1):10. doi: 10.1007/s13137-019-0120-z. Epub 2019 Jan 29.