A Semi-Lagrangian Approximation of Min–Max Type for the Stationary Mean Curvature Equation

E. Carlini () and R. Ferretti ()
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E. Carlini: Universitá di Roma “La Sapienza”, Dipartimento di Matematica
R. Ferretti: Universitá di Roma Tre, Dipartimento di Matematica

A chapter in Numerical Mathematics and Advanced Applications, 2008, pp 679-686 from Springer

Abstract: Abstract We propose a technique to treat degenerate elliptic equations, focusing on the model problem of the stationary Mean Curvature Motion equation in two space dimensions. This technique may be interpreted as a stationary, fully discrete version of the schemes proposed in slightly different forms by Catté et al. and by Kohn and Serfaty. We study consistency and monotonicity of the scheme and a correct implementation of Dirichlet boundary conditions. Numerical tests are also presented.

Date: 2008
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DOI: 10.1007/978-3-540-69777-0_81

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