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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.98.

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The discontinuous Galerkin method with diffusion
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by Gerard R. Richter PDF
Math. Comp. 58 (1992), 631-643 Request permission

Abstract:

We propose a way of extending the discontinuous Galerkin method from pure hyperbolic equations to convection-dominated equations with an $O(h)$ diffusion term. The resulting method is explicit and can be applied with polynomials of degree $n \geq 1$. The extended method satisfies the same $O({h^{n + 1/2}})$ error estimate previously established for the discontinuous Galerkin method as applied to hyperbolic problems. Numerical results are provided.
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Math. Comp. 58 (1992), 631-643
  • MSC: Primary 65M60; Secondary 65M15, 65N30, 76M25, 76Rxx
  • DOI: https://doi.org/10.1090/S0025-5718-1992-1122076-2
  • MathSciNet review: 1122076