On global error estimation and control of finite difference solutions for parabolic equations

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Abstract

The aim of this paper is to extend the global error estimation and control addressed in Lang and Verwer [SIAM J. Sci. Comput. 29, 2007] for initial value problems to finite difference solutions of parabolic partial differential equations. The classical ODE approach based on the first variational equation is combined with an estimation of the PDE spatial truncation error to estimate the overall error in the computed solution. Control in a discrete Lnorm is achieved through tolerance proportionality and mesh refinement. A numerical example illustrates the reliability of the estimation and control strategies.

OriginalsprogEngelsk
TitelAdaptive Modeling and Simulation 2013
RedaktørerJ. P. Moitinho de Almeida, P. Díez, C. Tiago, N. Parés
UdgivelsesstedBarcelona, Spain
ForlagInternational Center for Numerical Methods in Engineering
Publikationsdato2013
Sider187-198
StatusUdgivet - 2013

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