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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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An analysis of the discontinuous Galerkin method for a scalar hyperbolic equation
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by C. Johnson and J. Pitkäranta PDF
Math. Comp. 46 (1986), 1-26 Request permission

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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Additional Information
  • © Copyright 1986 American Mathematical Society
  • Journal: Math. Comp. 46 (1986), 1-26
  • MSC: Primary 65M60
  • DOI: https://doi.org/10.1090/S0025-5718-1986-0815828-4
  • MathSciNet review: 815828