ON NUMERICAL SCHEMES FOR SOLVING A NONLINEAR PDE WITH A MEAN CURVATURE TERM ON TRIANGULAR MESHES

Alexandra Claisse (1) , Pascal Frey (1)

1 LJLL - Laboratoire Jacques-Louis Lions

In this paper, we propose two numerical schemes for solving a nonlinear level set equation on unstructured triangulations. The consistency and the stability of these schemes are shown. In addition, we show how to compute nodewise fisrt and second order derivatives. An application example of curve construction using these approximations is provided to demonstrate their accuracy.

Mots clés: Analysis of a numerical scheme; Unstructured mesh; Level set method; Mean curvature evolution; Second order derivatives approximation; Non linear PDE problem; Curve reconstruction

Domaines: Analyse numérique [cs.NA]

Alexandra Claisse, Pascal Frey. ON NUMERICAL SCHEMES FOR SOLVING A NONLINEAR PDE WITH A MEAN CURVATURE TERM ON TRIANGULAR MESHES. 2009. ⟨hal-00391974⟩