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Nicolas Therme
A class of robust numerical schemes to compute front propagation
SMAI-Journal of computational mathematics, 4 (2018), p. 375-397, doi: 10.5802/smai-jcm.39
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Class. Math.: 35F21, 65N08, 65N12
Mots clés: Finite volumes, Hamilton-Jacobi, Stability, Convergence

Abstract

In this work a class of finite volume schemes is proposed to numerically solve equations involving propagating fronts. They fall into the class of Hamilton-Jacobi equations. Finite volume schemes based on staggered grids and initially developed to compute fluid flows, are adapted to the G-equation, using the Hamilton-Jacobi theoretical framework. The designed scheme has a maximum principle property and is consistent and monotonous on Cartesian grids. A convergence property is then obtained for the scheme on Cartesian grids and numerical experiments evidence the convergence of the scheme on more general meshes.

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