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

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

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.

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