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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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Error estimates for a nonlinear degenerate parabolic problem
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by P. Lesaint and J. Pousin PDF
Math. Comp. 59 (1992), 339-358 Request permission

Abstract:

In this paper we are dealing with a partial differential equation of parabolic type, which degenerates on one side of the domain. This equation may be viewed either as a model of particle diffusion in plasma physics, or as a simplified model of a viscous boundary layer in two dimensions. Known results for the existence and uniqueness of the weak solution are first recalled. A finite difference implicit scheme is then defined, and error bounds are derived, taking into account the low degree of smoothness of the exact solution. An iterative algorithm for the computation of the numerical solution at each time step is shown to be convergent.
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Additional Information
  • © Copyright 1992 American Mathematical Society
  • Journal: Math. Comp. 59 (1992), 339-358
  • MSC: Primary 35K65; Secondary 65M06, 65M12, 65M15, 76M25, 76X05
  • DOI: https://doi.org/10.1090/S0025-5718-1992-1134734-4
  • MathSciNet review: 1134734