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Approximation of the Velocity by Coupling Discontinuous Galerkin and Mixed Finite Element Methods for Flow Problems

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Abstract

In this paper, we show how to couple the local discontinuous Galerkin method and the Raviart–Thomas mixed finite element method for elliptic equations modeling flow problems. We then show that the approximation of the velocity converges with the optimal order of k when we take the local discontinuous Galerkin that uses polynomials of degree k and the Raviart–Thomas space of polynomials of degree k−1.

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Authors and Affiliations

  1. Department of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    Bernardo Cockburn

  2. Texas Institute for Computational and Applied Mathematics, The University of Texas at Austin, Austin, TX, 78712, USA

    Clint Dawson

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  1. Bernardo Cockburn
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Cockburn, B., Dawson, C. Approximation of the Velocity by Coupling Discontinuous Galerkin and Mixed Finite Element Methods for Flow Problems. Computational Geosciences 6, 505–522 (2002). https://doi.org/10.1023/A:1021203618109

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