# American Institute of Mathematical Sciences

January  2012, 11(1): 147-172. doi: 10.3934/cpaa.2012.11.147

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

 1 Université Paris-Est Marne-La-Vallée, 5 bd Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée Cedex 2 2 Slovak University of Technology, Slovak Republic, Slovak Republic

Received  December 2009 Revised  September 2010 Published  September 2011

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.
Citation: Robert Eymard, Angela Handlovičová, Karol Mikula. Approximation of nonlinear parabolic equations using a family of conformal and non-conformal schemes. Communications on Pure & Applied Analysis, 2012, 11 (1) : 147-172. doi: 10.3934/cpaa.2012.11.147
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