Finite difference methods for the Infinity Laplace and p-Laplace equations

Details Finite difference methods for the Infinity Laplace and p-Laplace equations Finite difference methods for the Infinity Laplace and p-Laplace equations

2011-07-26

arxiv.org/abs/1107.5278v2

Mathematics

Numerical Analysis

14 pages, 9 figures

Scientific paper

We build convergent discretizations and semi-implicit solvers for the Infinity Laplacian and the game theoretical $p$-Laplacian. The discretizations simplify and generalize earlier ones. We prove convergence of the solution of the Wide Stencil finite difference schemes to the unique viscosity solution of the underlying equation. We build a semi-implicit solver, which solves the Laplace equation as each step. It is fast in the sense that the number of iterations is independent of the problem size. This is an improvement over previous explicit solvers, which are slow due to the CFL-condition.

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