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Algorithm to adjust a model using an a posteriori estimate.
Abstract
In many fields of scientific computing, the equations are well known but the coefficients are usually empirical functions which depend on some parameters difficult the evaluate exactly. These functions are approximated and a modeling error is then committed. In this work we focus on the elliptic nonlinear equation, with coefficients changing the behaviour to an unknown value hs. These coefficients are then approximated. We prove an a priori and an a posteriori estimates on the modeling error. The later estimates allows us -via local indicators- to build an adaptive algorithm to control the modeling error and automatically determine the ”best” approximation of hs. Numerical results confirm the convergence of this procedure and the interest of this approach.
Keywords
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