An optimal-order error estimate for the discontinuous Galerkin method

Author:
Gerard R. Richter

Journal:
Math. Comp. **50** (1988), 75-88

MSC:
Primary 65M15; Secondary 65M60, 65N30

MathSciNet review:
917819

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Abstract: In this paper a new approach is developed for analyzing the discontinuous Galerkin method for hyperbolic equations. For a model problem in , the method is shown to converge at a rate when applied with *n*th degree polynomial approximations over a semiuniform triangulation, assuming sufficient regularity in the solution.

**[1]**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**, 10.1137/0724021**[2]**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**, 10.1090/S0025-5718-1986-0815828-4**[3]**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**, 10.1137/0720065**[4]**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), Math. Res. Center, Univ. of Wisconsin-Madison, Academic Press, New York, 1974, pp. 89–123. Publication No. 33. MR**0658142****[5]**W. H. Reed & T. R. Hill,*Triangular Mesh Methods for the Neutron Transport Equation*, Los Alamos Scientific Laboratory Report LA-UR-73-479.

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Additional Information

DOI:
http://dx.doi.org/10.1090/S0025-5718-1988-0917819-3

Keywords:
Finite element method,
hyperbolic equation

Article copyright:
© Copyright 1988
American Mathematical Society