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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.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


Optimal error estimates of the direct discontinuous Galerkin method for convection-diffusion equations
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by Hailiang Liu PDF
Math. Comp. 84 (2015), 2263-2295 Request permission


In this paper, we present the optimal $L^2$-error estimate of $O(h^{k+1})$ for polynomial elements of degree $k$ of the semidiscrete direct discontinuous Galerkin method for convection-diffusion equations. The main technical difficulty lies in the control of the inter-element jump terms which arise because of the convection and the discontinuous nature of numerical solutions. The main idea is to use some global projections satisfying interface conditions dictated by the choice of numerical fluxes so that trouble terms at the cell interfaces are eliminated or controlled. In multi-dimensional case, the orders of $k+1$ hinge on a superconvergence estimate when tensor product polynomials of degree $k$ are used on Cartesian grids. A collection of projection errors in both one- and multi-dimensional cases is established.
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Additional Information
  • Hailiang Liu
  • Affiliation: Department of Mathematics, Iowa State University, Ames, Iowa 50010
  • Email:
  • Received by editor(s): February 19, 2013
  • Received by editor(s) in revised form: August 13, 2013, and December 12, 2013
  • Published electronically: February 17, 2015
  • © Copyright 2015 American Mathematical Society
  • Journal: Math. Comp. 84 (2015), 2263-2295
  • MSC (2010): Primary 35K15, 65M15, 65M60, 76R50
  • DOI:
  • MathSciNet review: 3356026