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Mathematics of Computation

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Error estimates for a nonlinear degenerate parabolic problem

Authors: P. Lesaint and J. Pousin
Journal: Math. Comp. 59 (1992), 339-358
MSC: Primary 35K65; Secondary 65M06, 65M12, 65M15, 76M25, 76X05
MathSciNet review: 1134734
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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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Keywords: Numerical analysis, nonlinear, parabolic equation, finite differences, error estimates
Article copyright: © Copyright 1992 American Mathematical Society