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Mathematics of Computation

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

Authors: Bernardo Cockburn, Suchung Hou and Chi-Wang Shu
Journal: Math. Comp. 54 (1990), 545-581
MSC: Primary 65M60; Secondary 35L65, 65N30
MathSciNet review: 1010597
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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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Keywords: Discontinuous finite elements, local projection, multidimensional conservation laws
Article copyright: © Copyright 1990 American Mathematical Society