Cockburn, Bernardo; Hou, Suchung; Shu, Chi-Wang The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. IV: The multidimensional case. (English) Zbl 0695.65066 Math. Comput. 54, No. 190, 545-581 (1990). 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. Cited in 3 ReviewsCited in 570 Documents 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 Keywords:conservation laws; two-dimensional; Runge-Kutta local projection discontinuous Galerkin methods; general triangulations; maximum principles; numerical results Citations:Zbl 0677.65093 PDF BibTeX XML Cite \textit{B. Cockburn} et al., Math. Comput. 54, No. 190, 545--581 (1990; Zbl 0695.65066) Full Text: DOI Link OpenURL