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A coupling of mixed and continuous Galerkin finite element methods for poroelasticity I: the continuous in time case

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Abstract

In this paper, we formulate a finite element procedure for approximating the coupled fluid and mechanics in Biot’s consolidation model of poroelasticity. Here, we approximate the pressure by a mixed finite element method and the displacements by a Galerkin method. Theoretical convergence error estimates are derived in a continuous in-time setting for a strictly positive constrained specific storage coefficient. Of particular interest is the case when the lowest-order Raviart–Thomas approximating space or cell-centered finite differences are used in the mixed formulation, and continuous piecewise linear approximations are used for displacements. This approach appears to be the one most frequently applied to existing reservoir engineering simulators.

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Authors and Affiliations

  1. Center for Subsurface Modeling (CSM), Institute for Computational Engineering and Sciences (ICES), University of Texas at Austin, Austin, TX, USA

    Phillip Joseph Phillips

  2. CSM, ICES, Department of Aerospace Engineering and Engineering Mechanics, University of Texas at Austin, Austin, TX, USA

    Mary F. Wheeler

  3. Department of Petroleum Engineering and Geosystems Engineering, University of Texas at Austin, Austin, TX, USA

    Mary F. Wheeler

  4. Institute for Computational Engineering and Sciences, University of Texas at Austin, Austin, TX, USA

    Mary F. Wheeler

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  1. Phillip Joseph Phillips
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Correspondence to Mary F. Wheeler.

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Phillips, P.J., Wheeler, M.F. A coupling of mixed and continuous Galerkin finite element methods for poroelasticity I: the continuous in time case. Comput Geosci 11, 131–144 (2007). https://doi.org/10.1007/s10596-007-9045-y

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  • DOI: https://doi.org/10.1007/s10596-007-9045-y

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