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

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

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]**R. S. Falk & G. R. Richter, "Analysis of a continuous finite element method for hyperbolic equations,"*SIAM J. Numer. Anal.*, v. 24, 1987, pp. 257-278. MR**881364 (88d:65133)****[2]**C. Johnson & J. Pitkäranta, "An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation,"*Math. Comp.*, v. 46, 1986, pp. 1-26. MR**815828 (88b:65109)****[3]**C. Johnson & J. Pitkäranta, "Convergence of a fully discrete scheme for two-dimensional neutron transport,"*SIAM J. Numer. Anal.*, v. 20, 1983, pp. 951-966. MR**714690 (85c:82082)****[4]**P. Lesaint & P. A. Raviart, "On a finite element method for solving the neutron transport equation," in*Mathematical Aspects of Finite Elements in Partial Differential Equations*(C. deBoor, ed.), Academic Press, New York, 1974, pp. 89-123. MR**0658142 (58:31918)****[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:
https://doi.org/10.1090/S0025-5718-1988-0917819-3

Keywords:
Finite element method,
hyperbolic equation

Article copyright:
© Copyright 1988
American Mathematical Society