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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.

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.

 

An efficient linear scheme to approximate parabolic free boundary problems: error estimates and implementation
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by Ricardo H. Nochetto and Claudio Verdi PDF
Math. Comp. 51 (1988), 27-53 Request permission

Abstract:

This paper deals with a fully discrete scheme to approximate multidimensional singular parabolic problems; two-phase Stefan problems and porous medium equations are included. The algorithm consists of approximating at each time step a linear elliptic partial differential equation by piecewise linear finite elements and then making an element-by-element algebraic correction to account for the nonlinearity. Several energy error estimates are derived for the physical unknowns; a sharp rate of convergence of $O({h^{1/2}})$ is our main result. The crucial point in implementing the scheme is the efficient resolution of linear systems involved. This topic is discussed, and the results of several numerical experiments are shown.
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Additional Information
  • © Copyright 1988 American Mathematical Society
  • Journal: Math. Comp. 51 (1988), 27-53
  • MSC: Primary 65N15; Secondary 65N30
  • DOI: https://doi.org/10.1090/S0025-5718-1988-0942142-0
  • MathSciNet review: 942142