A Posteriori Control of Modeling Errors and Discretization Errors
Abstract
We investigate the concept of dual-weighted residuals for measuring model errors in the numerical solution of nonlinear partial differential equations. The method is first derived in the case where only model errors arise and then extended to handle simultaneously model and discretization errors. We next present an adaptive model/mesh refinement procedure where both sources of error are equilibrated. Various test cases involving Poisson equations and convection-diffusion-reaction equations with complex diffusion models (oscillating diffusion coefficient, nonlinear diffusion, multicomponent diffusion matrix) confirm the reliability of the analysis and the efficiency of the proposed methodology.
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Published In
Multiscale Modeling & Simulation
Pages: 221 - 238
ISSN (online): 1540-3467
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Copyright © 2003 Society for Industrial and Applied Mathematics.
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Published online: 26 July 2006
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