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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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Convergence of a step-doubling Galerkin method for parabolic problems
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by Bruce P. Ayati and Todd F. Dupont PDF
Math. Comp. 74 (2005), 1053-1065 Request permission

Abstract:

We analyze a single step method for solving second-order parabolic initial–boundary value problems. The method uses a step-doubling extrapolation scheme in time based on backward Euler and a Galerkin approximation in space. The technique is shown to be a second-order correct approximation in time. Since step-doubling can be used as a mechanism for step-size control, the analysis is done for variable time steps. The stability properties of step-doubling are contrasted with those of Crank-Nicolson, as well as those of more general extrapolated theta-weighted schemes. We provide an example computation that illustrates both the use of step-doubling for adaptive time step control and the application of step-doubling to a nonlinear system.
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Additional Information
  • Bruce P. Ayati
  • Affiliation: Department of Mathematics, Southern Methodist University, Dallas, Texas 75275
  • Email: ayati@smu.edu
  • Todd F. Dupont
  • Affiliation: Departments of Computer Science and Mathematics, The University of Chicago, Chicago, Illinois 60637
  • Email: dupont@cs.uchicago.edu
  • Received by editor(s): October 22, 2003
  • Received by editor(s) in revised form: February 27, 2004
  • Published electronically: September 10, 2004
  • Additional Notes: The second author was supported by the ASCI Flash Center at the University of Chicago under DOE contract B532820, and by the MRSEC Program of the National Science Foundation under award DMR-0213745.
  • © Copyright 2004 American Mathematical Society
  • Journal: Math. Comp. 74 (2005), 1053-1065
  • MSC (2000): Primary 65M06, 65M12, 65M60; Secondary 35K15, 35K20, 65M15
  • DOI: https://doi.org/10.1090/S0025-5718-04-01696-5
  • MathSciNet review: 2136993