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

Author:

Cockburn Bernardo,Hou Suchung,Shu Chi-Wang

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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,Computational Mathematics,Algebra and Number Theory

Reference43 articles.

1. First order quasilinear equations with boundary conditions;Bardos, C.;Comm. Partial Differential Equations,1979

2. J. B. Bell, C. N. Dawson, and G. R. Shubin, An unsplit, higher-order Godunov method for scalar conservation laws in multiple dimensions, J. Comput. Phys. 74 (1988), 1-24.

3. G. Chavent, B. Cockburn, G. Cohen, and J. Jaffré, A discontinuous finite element method for nonlinear hyperbolic equations, Innovative Numerical Methods in Engineering (Proc. 4th Internat. Sympos. (Georgia Institute of Technology, Atlanta, Georgia), Springer-Verlag, 1986, pp. 337-342.

4. Studies in Mathematics and its Applications, Vol. 4;Ciarlet, Philippe G.,1978

5. B. Cockburn and C.-W. Shu, The Runge—Kutta local projection 𝑃¹ discontinuous Galerkin finite element method for scalar conservation laws, Institute for Mathematics and its Applications Preprint Series # 388, Univ. of Minnesota (1988); Proceedings of First National Fluid Dynamics Congress, Cincinnati, Ohio, July 24-28, 1988; to appear in 𝑀²𝐴𝑁.

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