Damping, Stabilization and Numerical Filtering for the Modeling and the Simulation of time dependent PDEs
Amortissement, stabilisation et filtrage numérique pour la modélisation et la simulation d'EDP d'évolution
Résumé
We present here different situations in which the filtering of high or low modes is used either for stabilizing semi-implicit numerical schemes when solving nonlinear parabolic equations, either for building adapted damping operators in the case of dispersive equation. We consider numerical filtering provided by mutigrid-like techniques as well as the filtering resulting from operator with monotone symbols. Our approach applies to several discretization techniques and we focus on finite elements and finite differences. Numerical illustrations are given on Cahn-Hilliard, Korteweig-de-Vries and Ku-ramoto Sivashinsky equations. In memory of Ezzeddine Zahrouni
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