an:04139238
Zbl 0695.65066
Cockburn, Bernardo; Hou, Suchung; Shu, Chi-Wang
The Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. IV: The multidimensional case
EN
Math. Comput. 54, No. 190, 545-581 (1990).
00173800
1990
j
65N30 65M60 35L65
conservation laws; two-dimensional; Runge-Kutta local projection discontinuous Galerkin methods; general triangulations; maximum principles; numerical results
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.
Zbl 0677.65093