The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. IV. The multidimensional case

Cockburn, Bernardo; Hou, Suchung; Shu, Chi-Wang

doi:10.1090/S0025-5718-1990-1010597-0

The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. IV. The multidimensional case
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by Bernardo Cockburn, Suchung Hou and Chi-Wang Shu PDF

Math. Comp. 54 (1990), 545-581 Request permission

Abstract:

In this paper we study the two-dimensional version of the Runge-Kutta Local Projection Discontinuous Galerkin (RKDG) methods, already defined and analyzed in the one-dimensional case. These schemes are defined on general triangulations. They can easily handle the boundary conditions, verify maximum principles, and are formally uniformly high-ordrr accurate. Preliminary numerical results showing the performance of the schemes on a variety of initial-boundary value problems are shown.

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