A vertex-centered, dual discontinuous Galerkin method

  • Authors:

  • Martin Berggren

  • Affiliations:

  • Department of Information Technology, Uppsala University, Sweden and Division of Aeronautics FFA, FOI, the Swedish Defence Research Agency, Sweden

  • Venue:
  • Journal of Computational and Applied Mathematics - Special issue on computational and mathematical methods in science and engineering (CMMSE-2004)
  • Year:
  • 2006

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Abstract

This note introduces a new version of the discontinuous Galerkin method for discretizing first-order hyperbolic partial differential equations. The method uses piecewise polynomials that are continuous on a macroelement surrounding the nodes in the unstructured mesh but discontinuous between the macroelements. At lowest order, the method reduces to a vertex-centered finite-volume method with control volumes based on a dual mesh, and the method can be implemented using an edge-based data structure. The method provides therefore a strategy to extend existing vertex-centered finite-volume codes to higher order using the discontinuous Galerkin method. Preliminary tests on a model linear hyperbolic equation in two-dimensional indicate a favorable qualitative behavior for nonsmooth solutions and optimal convergence rates for smooth solutions.