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Mathematics of Computation

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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.

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