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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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Implicit-explicit multistep finite element methods for nonlinear parabolic problems
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by Georgios Akrivis, Michel Crouzeix and Charalambos Makridakis PDF
Math. Comp. 67 (1998), 457-477 Request permission


We approximate the solution of initial boundary value problems for nonlinear parabolic equations. In space we discretize by finite element methods. The discretization in time is based on linear multistep schemes. One part of the equation is discretized implicitly and the other explicitly. The resulting schemes are stable, consistent and very efficient, since their implementation requires at each time step the solution of a linear system with the same matrix for all time levels. We derive optimal order error estimates. The abstract results are applied to the Kuramoto-Sivashinsky and the Cahn-Hilliard equations in one dimension, as well as to a class of reaction diffusion equations in ${\mathbb {R}} ^{\nu },$ $\nu = 2, 3.$
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Additional Information
  • Georgios Akrivis
  • Affiliation: Department of Computer Science, University of Ioannina, 451 10 Ioannina, Greece
  • MR Author ID: 24080
  • Email:
  • Michel Crouzeix
  • Affiliation: IRMAR, Université de Rennes I, Campus de Beaulieu, F-35042 Rennes, France
  • Email:
  • Charalambos Makridakis
  • Affiliation: Department of Mathematics, University of Crete, 714 09 Heraklion, Crete, Greece, and IACM, Foundation for Research and Technology - Hellas, 711 10 Heraklion, Crete, Greece
  • MR Author ID: 289627
  • Email:
  • Received by editor(s): July 3, 1995
  • Received by editor(s) in revised form: December 8, 1995
  • Additional Notes: The work of the first and third authors was supported in part by a research grant from the University of Crete
  • © Copyright 1998 American Mathematical Society
  • Journal: Math. Comp. 67 (1998), 457-477
  • MSC (1991): Primary 65M60, 65M12; Secondary 65L06
  • DOI:
  • MathSciNet review: 1458216