Applications of approximate gradient schemes for nonlinear parabolic equations

Robert Eymard (1) , Angela Handlovicova (2, 3) , Raphaèle Herbin (4) , Karol Mikula (2, 3) , O. Stašová (3)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 STUBA - Department of Mathematics
3 Department of Mathematics, Slovak University of Technology
4 LATP - Laboratoire d'Analyse, Topologie, Probabilités

We propose the use of gradient schemes for the approximation of possibly non-local regularizations of the Perona-Malik equations. We then prove the convergence of this method thanks to compactness arguments, and we apply it to a particular gradient scheme on rectangular meshes, whose advantage is to lead to nine-point stencil matrices. Numerical examples provide indications about the accuracy of the method.

Domaines: Analyse numérique [math.NA]

Robert Eymard, Angela Handlovicova, Raphaèle Herbin, Karol Mikula, O. Stašová. Applications of approximate gradient schemes for nonlinear parabolic equations. Applications of Mathematics, 2015, ⟨10.1007/s10492-015-0088-4⟩. ⟨hal-00744767⟩