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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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A stable extrapolation method for multidimensional degenerate parabolic problems
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by Ricardo H. Nochetto PDF
Math. Comp. 53 (1989), 455-470 Request permission

Abstract:

Degenerate parabolic problems in several space variables are approximated by combining a preliminary regularization procedure with a finite element extrapolation method. The proposed extrapolation acts on the so-called phase variable and leads to a linear problem which is shown to be stable. The ensuing linear algebraic system involves the same matrix for all time steps. Energy error estimates are also derived for the physical unknowns. An $O({h^{1/2}})$ rate of convergence is proved, provided the approximation parameters are suitably related. In case the linear systems are solved by an iterative algorithm, such as the conjugate gradient method, an $O({h^{3/2}})$ tolerance for the error reduction is shown to preserve the overall accuracy; the required computational effort is thus nearly optimal.
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Additional Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Math. Comp. 53 (1989), 455-470
  • MSC: Primary 65N30; Secondary 35K55, 35K65, 65N15
  • DOI: https://doi.org/10.1090/S0025-5718-1989-0982372-6
  • MathSciNet review: 982372