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An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation

Authors: C. Johnson and J. Pitkäranta
Journal: Math. Comp. 46 (1986), 1-26
MSC: Primary 65M60
MathSciNet review: 815828
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Abstract: We prove $ {L_p}$ stability and error estimates for the discontinuous Galerkin method when applied to a scalar linear hyperbolic equation on a convex polygonal plane domain. Using finite element analysis techniques, we obtain $ {L_2}$ estimates that are valid on an arbitrary locally regular triangulation of the domain and for an arbitrary degree of polynomials. $ {L_p}$ estimates for $ p \ne 2$ are restricted to either a uniform or piecewise uniform triangulation and to polynomials of not higher than first degree. The latter estimates are proved by combining finite difference and finite element analysis techniques.

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Article copyright: © Copyright 1986 American Mathematical Society