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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 $ {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 [Enhancements On Off] (What's this?)

  • [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)
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  • [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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Keywords: Finite element method, hyperbolic equation
Article copyright: © Copyright 1988 American Mathematical Society

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