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A Combined Mixed Hybrid and Hybridizable Discontinuous Galerkin Method for Darcy Flow and Transport

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Abstract

A combined hybrid mixed and hybridizable discontinuous Galerkin method is formulated for the flow and transport equations. Convergence of the method is obtained by deriving optimal a priori error bounds in the L\(^2\) norm in space. Since the velocity in the transport equation depends on the flow problem, the stabilization parameter in the HDG method is a function of the discrete velocity. In addition, a key ingredient in the convergence proof is the construction of a projection that is shown to satisfy optimal approximation bounds. Numerical examples confirm the theoretical convergence rates and show the efficiency of high order discontinuous elements.

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Funding

Keegan L. A. Kirk gratefully acknowledges support from the Natural Sciences and Engineering Research Council of Canada through the Postdoctoral Fellowship Program (PDF-568008); Beatrice Riviere gratefully acknowledges support from the National Science Foundation NSF-DMS 2111459.

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  1. Department of Computational Applied Mathematics and Operations Research, Rice University, Houston, TX, 77005, USA

    Keegan L. A. Kirk & Beatrice Riviere

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  1. Keegan L. A. Kirk
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Correspondence to Keegan L. A. Kirk.

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Kirk, K.L.A., Riviere, B. A Combined Mixed Hybrid and Hybridizable Discontinuous Galerkin Method for Darcy Flow and Transport. J Sci Comput 100, 57 (2024). https://doi.org/10.1007/s10915-024-02607-0

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