Approximation of nonlinear parabolic equations using a family of conformal and non-conformal schemes

Robert Eymard (1) , Angela Handlovicova (2) , Karol Mikula (2)

1 LAMA - Laboratoire d'Analyse et de Mathématiques Appliquées
2 STUBA - Department of Mathematics

We consider a family of space discretisations for the approximation of nonlinear parabolic equations, such as the regularised mean curvature flow level set equation, using semi-implicit or fully implicit time schemes. The approximate solution provided by such a scheme is shown to converge thanks to compactness and monotony arguments. Numerical examples show the accuracy of the method.

Mots clés: conformal finite element scheme; non-conformal finite element scheme; convergence of the scheme; nonlinear parabolic equation

Domaines: Analyse numérique [math.NA]

Robert Eymard, Angela Handlovicova, Karol Mikula. Approximation of nonlinear parabolic equations using a family of conformal and non-conformal schemes. Communications on Pure and Applied Mathematics, 2012, 11 (1), http://www.aimsciences.org/journals/displayArticlesnew.jsp?paperID=6484. ⟨10.3934/cpaa.2012.11.147⟩. ⟨hal-00453537⟩