On Global Error Estimation and Control of Finite Difference Solutions for Parabolic Equations

Details On Global Error Estimation and Control of Finite Difference Solutions for Parabolic Equations On Global Error Estimation and Control of Finite Difference Solutions for Parabolic Equations

2009-11-13

arxiv.org/abs/0911.2656v1

Mathematics

Numerical Analysis

Scientific paper

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 $L_2$-norm is achieved through tolerance proportionality and mesh refinement. Numerical examples are used to illustrate the reliability of the estimation and control strategies.

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