Continuous, discontinuous and coupled discontinuous–continuous Galerkin finite element methods for the shallow water equations

Authors

  • Clint Dawson,

    1. Institute for Computational Engineering and Sciences, University of Texas, Austin, TX 78712-1528, U.S.A.
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  • Joannes J. Westerink,

    Corresponding author
    1. Department of Civil Engineering and Geological Sciences, University of Notre Dame, Notre Dame, IN 46556-5602, U.S.A.
    • Department of Civil Engineering and Geological Sciences, University of Notre Dame, 156 Fitzpatrick Hall, Notre Dame, IN 46556-5602, U.S.A.
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  • Jesse C. Feyen,

    1. Department of Civil Engineering and Geological Sciences, University of Notre Dame, Notre Dame, IN 46556-5602, U.S.A.
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  • Dharhas Pothina

    1. Institute for Computational Engineering and Sciences, University of Texas, Austin, TX 78712-1528, U.S.A.
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Abstract

We consider the approximation of the depth-averaged two-dimensional shallow water equations by both a traditional continuous Galerkin (CG) finite element method as well as two discontinuous Galerkin (DG) approaches. The DG method is locally conservative, flux-continuous on each element edge, and is suitable for both smooth and highly advective flows. A novel technique of coupling a DG method for continuity with a CG method for momentum is developed. This formulation is described in detail and validation via numerical testing is presented. Comparisons between a widely used CG approach, a conventional DG method, and the novel coupled discontinuous–continuous Galerkin method illustrates advantages and disadvantages in accuracy and efficiency. Copyright © 2006 John Wiley & Sons, Ltd.

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