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 Catte 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.
A Semi-Lagrangian approximation of min-max type for the stationary mean curvature equation / Carlini, Elisabetta; R., Ferretti. - (2008), pp. 679-686. (Intervento presentato al convegno ENUMATH 2007, the 7th European Conference on Numerical Mathematics and Advanced Applications tenutosi a Graz (Austria)) [10.1007/978-3-540-69777-0_81].
A Semi-Lagrangian approximation of min-max type for the stationary mean curvature equation
CARLINI, Elisabetta;
2008
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 Catte 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.| File | Dimensione | Formato | |
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