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Locking-Free and Locally-Conservative Enriched Galerkin Method for Poroelasticity

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Abstract

This paper develops a new coupled enriched Galerkin (EG) scheme for Biot’s poroelasticity model based on the displacement-pressure formulation. The aim of this work is to provide a stable and robust numerical method for a wide range of physical and numerical parameters. The finite-dimensional solution spaces are enriched linear Lagrange spaces, and the inf-sup condition between the two spaces is achieved by adding a stabilization term. The resulting coupled EG method is locally conservative and provides stable solutions without spurious oscillations or overshoots/undershoots. The well-posedness and optimal a priori error estimates are established. Numerical results in various scenarios are provided.

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Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Funding

The work of S. Lee was partially supported by the U.S. National Science Foundation Grant DMS-1913016 and DMS-2208402. The work of S.-Y. Yi was supported by the U.S. National Science Foundation under Grant DMS-2208426.

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Authors and Affiliations

  1. Department of Mathematics, Florida State University, Tallahassee, FL, 32306, USA

    Sanghyun Lee

  2. Department of Mathematical Sciences, University of Texas at El Paso, El Paso, TX, 79968, USA

    Son-Young Yi

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Lee, S., Yi, SY. Locking-Free and Locally-Conservative Enriched Galerkin Method for Poroelasticity. J Sci Comput 94, 26 (2023). https://doi.org/10.1007/s10915-022-02079-0

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