A Stabilized Hybrid Mixed Finite Element Method for Poroelasticity (Record no. 708)

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fixed length control field 250101s2019 xx o 000 0 eng d
100 1# - MAIN ENTRY--PERSONAL NAME
Personal name Chunyan Niu
245 10 - TITLE STATEMENT
Title A Stabilized Hybrid Mixed Finite Element Method for Poroelasticity
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Name of producer, publisher, distributor, manufacturer arXiv
Date of production, publication, distribution, manufacture, or copyright notice 2019
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Content type term text
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Carrier type term online resource
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Summary, etc. In this work, we consider a hybrid mixed finite element method for Biot's model. The hybrid P1-RT0-P0 discretization of the displacement-pressure-Darcy's velocity system of Biot's model presented in \cite{C. Niu} is not uniformly stable with respect to the physical parameters, resulting in some issues in numerical simulations. To alleviate such problems, following \cite{V. Girault}, we stabilize the hybrid scheme with face bubble functions and show the well-posedness with respect to physical and discretization parameters, which provide optimal error estimates of the stabilized method. We introduce a perturbation of the bilinear form of the displacement which allows for the elimination of the bubble functions. Together with eliminating Darcy's velocity by hybridization, we obtain an eliminated system whose size is the same as the classical P1-RT0-P0 discretization. Based on the well-posed
506 0# - RESTRICTIONS ON ACCESS NOTE
Terms governing access Open access — freely available to read.
856 40 - ELECTRONIC LOCATION AND ACCESS
Uniform Resource Identifier <a href="https://arxiv.org/pdf/1906.00885v2">https://arxiv.org/pdf/1906.00885v2</a>
Link text Read the full paper (PDF)
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      Available online General Yegates University Library Yegates University Library Science and Computing 09/01/2026   YGE000969 09/01/2026 https://arxiv.org/pdf/1906.00885v2 09/01/2026 Research paper — read online