Approximation of nonlinear parabolic equations usinga family of conformal and non-conformal schemes

Robert Eymard; Angela Handlovičová; Karol Mikula

doi:10.3934/cpaa.2012.11.147

Article Contents

2012, Volume 11, Issue 1: 147-172. Doi: 10.3934/cpaa.2012.11.147

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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

Received: November 30, 2009

Revised: August 31, 2010

Published: December 2011

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Abstract

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.

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Mathematics Subject Classification: Primary: 65M08; Secondary: 35K93.

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References

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