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A posteriori error estimate for finite volume approximations of convection diffusion problems. (English) Zbl 1060.65103

Herbin, Raphaéle (ed.) et al., Finite volumes for complex applications III. Problems and perspectives. Papers from the 3rd symposium of finite volumes for complex applications, Porquerolles, France, June 24–28, 2002. London: Hermes Penton Science (ISBN 1-9039-9634-1/pbk). 753-760 (2002).
Summary: We deduce an a posteriori error estimate for cell centered finite volume approximations of nonlinear degenerate parabolic equations. The error estimator is robust with respect to the diffusion coefficient (which may tend to \(0\)) and is applicable either in the case of diffusion dominated or in the case of convection dominated solutions.
For the entire collection see [Zbl 1049.65002].

MSC:

65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35K55 Nonlinear parabolic equations
35K65 Degenerate parabolic equations
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