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The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. IV: The multidimensional case. (English) Zbl 0695.65066

Summary: [For part III see J. Comput. Phys. 84, No.1, 90-113 (1989; Zbl 0677.65093).]
We study the two-dimensional version of the Runge-Kutta local projection discontinuous Galerkin 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-order accurate. Preliminary numerical results showing the performance of the schemes on a variety of initial-boundary value problems are shown.

MSC:

65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws

Citations:

Zbl 0677.65093
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