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Physics-preserving enriched Galerkin method for a fully-coupled thermo-poroelasticity model

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Abstract

This paper proposes a new numerical method for a fully-coupled, quasi-static thermo-poroelasticity model in a unified enriched Galerkin (EG) method framework. In our method, the mechanics sub-problem is solved using a locking-free EG method, and the flow and heat sub-problems are solved using a locally-conservative EG method. The proposed method offers mass and energy conservation properties with much lower costs than other methods with the same properties, including discontinuous Galerkin methods and mixed finite element methods. The well-posedness and optimal a priori error estimates are carefully derived. Several numerical tests confirm the theoretical optimal convergence rates and the mass and energy conservation properties of the new method.

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Acknowledgements

The work of S.-Y. Yi was partially supported by the U.S. National Science Foundation under Grant DMS-2208426 and by the U.S. Department of Energy, Office of Science, Energy Earthshots Initiatives under Award Number DE-SC-0024703. The work of S. Lee was partially supported by the U.S. National Science Foundation Grant DMS-2208402 and by the U.S. Department of Energy, Office of Science, Energy Earthshots Initiatives under Award Number DE-SC-0024703.

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  1. Department of Mathematical Sciences, University of Texas at El Paso, 500 W University Ave, El Paso, TX, 79968, USA

    Son-Young Yi

  2. Department of Mathematics, Florida State University, 1017 Academic Way, Tallahassee, FL, 32304, USA

    Sanghyun Lee

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  1. Son-Young Yi
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Correspondence to Sanghyun Lee.

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Yi, SY., Lee, S. Physics-preserving enriched Galerkin method for a fully-coupled thermo-poroelasticity model. Numer. Math. 156, 949–978 (2024). https://doi.org/10.1007/s00211-024-01406-x

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