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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.


Discontinuous Galerkin method in time combined with a stabilized finite element method in space for linear first-order PDEs
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by Alexandre Ern and Friedhelm Schieweck PDF
Math. Comp. 85 (2016), 2099-2129 Request permission


We analyze the discontinuous Galerkin method in time combined with a finite element method with symmetric stabilization in space to approximate evolution problems with a linear, first-order differential operator. A unified analysis is presented for space discretization, including the discontinuous Galerkin method and $H^1$-conforming finite elements with interior penalty on gradient jumps. Our main results are error estimates in various norms for smooth solutions. Two key ingredients are the post-processing of the fully discrete solution by lifting its jumps in time and a new time-interpolate of the exact solution. We first analyze the $L^\infty (L^2)$ (at discrete time nodes) and $L^2(L^2)$ errors and derive a superconvergent bound of order $(\tau ^{k+2}+h^{r+1/2})$ for static meshes for $k\ge 1$. Here, $\tau$ is the time step, $k$ the polynomial order in time, $h$ the size of the space mesh, and $r$ the polynomial order in space. For the case of dynamically changing meshes, we derive a novel bound on the resulting projection error. Finally, we prove new optimal bounds on static meshes for the error in the time-derivative and in the discrete graph norm.
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Additional Information
  • Alexandre Ern
  • Affiliation: Universite Paris-Est, CERMICS (ENPC), 77455 Marne la Vallee Cedex 2, France
  • MR Author ID: 349433
  • Email:
  • Friedhelm Schieweck
  • Affiliation: Institut für Analysis und Numerik, Otto–von–Guericke–Universität Magdeburg, Postfach 4120, D-39016 Magdeburg, Germany
  • MR Author ID: 155960
  • Email:
  • Received by editor(s): February 18, 2014
  • Received by editor(s) in revised form: April 14, 2015
  • Published electronically: January 11, 2016
  • © Copyright 2016 American Mathematical Society
  • Journal: Math. Comp. 85 (2016), 2099-2129
  • MSC (2010): Primary 65M12, 65M60; Secondary 65J10
  • DOI:
  • MathSciNet review: 3511276