The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. IV. The multidimensional case
Bernardo Cockburn, Suchung Hou, Chi-Wang Shu
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Source: Crossref
Published: Jan 1, 1990
DOI: 10.1090/s0025-5718-1990-1010597-0
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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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