An optimal-order error estimate for the discontinuous Galerkin method

Richter, Gerard R.

doi:10.1090/S0025-5718-1988-0917819-3

An optimal-order error estimate for the discontinuous Galerkin method
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by Gerard R. Richter PDF

Math. Comp. 50 (1988), 75-88 Request permission

Abstract:

In this paper a new approach is developed for analyzing the discontinuous Galerkin method for hyperbolic equations. For a model problem in ${R^2}$, the method is shown to converge at a rate $O({h^{n + 1}})$ when applied with nth degree polynomial approximations over a semiuniform triangulation, assuming sufficient regularity in the solution.

References

Richard S. Falk and Gerard R. Richter, Analysis of a continuous finite element method for hyperbolic equations, SIAM J. Numer. Anal. 24 (1987), no. 2, 257–278. MR 881364, DOI 10.1137/0724021
C. Johnson and J. Pitkäranta, An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation, Math. Comp. 46 (1986), no. 173, 1–26. MR 815828, DOI 10.1090/S0025-5718-1986-0815828-4
Claes Johnson and Juhani Pitkäranta, Convergence of a fully discrete scheme for two-dimensional neutron transport, SIAM J. Numer. Anal. 20 (1983), no. 5, 951–966. MR 714690, DOI 10.1137/0720065
P. Lasaint and P.-A. Raviart, On a finite element method for solving the neutron transport equation, Mathematical aspects of finite elements in partial differential equations (Proc. Sympos., Math. Res. Center, Univ. Wisconsin, Madison, Wis., 1974) Publication No. 33, Math. Res. Center, Univ. of Wisconsin-Madison, Academic Press, New York, 1974, pp. 89–123. MR 0658142

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