The Runge-Kutta local projection p1-discontinuous-Galerkin finite element method for scalar conservation laws

Bernardo Cockburn, Chi Wang Shu

Research output: Contribution to conferencePaperpeer-review

Abstract

In this work we introduce and analize a new explicit method for solving numerically scalar conservation laws. The time-discretization of the method is based on a second order accurate TVD Runge-Kutta technique (used recently by Osher and Shu to solve scalar conservation laws in the framework of finite difference schemes), while the space-discretization is based on a discontinuous finite element method for which the approximate solution is taken to be piecewise linear in space (i. e., the local projection P0P1 -discontinuous Galerkin method introduced recently by Chavent and Cockbum). The resulting scheme is TVBM (total variation bounded in the means), converges to a weak solution, and is formally second order accurate in time and space for cfl ε [0, 1/3]. We give extensive numerical evidence that the scheme does converge to the entropy solution, and that the order of convergence away from singularities is optimal; i. e., equal to 2 in the norm of L(Lloc).

Original languageEnglish (US)
StatePublished - Jan 1 1988
Event1st National Fluid Dynamics Conference, 1988 - Cincinnati, United States
Duration: Jul 25 1988Jul 28 1988

Other

Other1st National Fluid Dynamics Conference, 1988
CountryUnited States
CityCincinnati
Period7/25/887/28/88

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