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Origins, analysis, numerical analysis, and numerical approximation of a forward-backward parabolic problem

Published online by Cambridge University Press:  15 August 2002

A. Kadir Aziz ,
Donald A. French ,
Soren Jensen  and
R. Bruce Kellogg
A. Kadir Aziz
Affiliation:
Department of Mathematics, UMBC, Baltimore, MD 21250, USA. aziz@math.umbc.edu.
Donald A. French
Affiliation:
Department of Mathematics, UMBC, Baltimore, MD 21250, USA. aziz@math.umbc.edu. Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH 45221, USA. french@math.uc.edu.
Soren Jensen
Affiliation:
Department of Mathematics, UMBC, Baltimore, MD 21250, USA. aziz@math.umbc.edu.
R. Bruce Kellogg
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD 20742, USA. kellogg@ipst.umd.edu.
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Abstract

We consider the analysis and numerical solution of a forward-backward boundary value problem. We provide some motivation, prove existence and uniqueness in a function class especially geared to the problem at hand, provide various energy estimates, prove a priori error estimates for the Galerkin method, and show the results of some numerical computations.

Keywords

Forward-backwardheat equationdegenerate parabolic problemBrownian motionelectron and neutron scatteringseparated flow boundary layers.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 33 , Issue 5 , September 1999 , pp. 895 - 922
Copyright
© EDP Sciences, SMAI, 1999

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