Geodesic
A class of robust numerical schemes to compute front propagation
Therme, Nicolas1
1 Université de Nantes, Laboratoire de Mathématiques Jean Leray, CNRS UMR 6629, 2 rue de la Houssinière, BP 92208, 44322 Nantes, France
The SMAI Journal of computational mathematics, Tome 4 (2018), pp. 375-397

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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.

Publié le :
DOI : 10.5802/smai-jcm.39
Classification : 35F21, 65N08, 65N12
Keywords: Finite volumes, Hamilton-Jacobi, Stability, Convergence

Therme, Nicolas 1

1 Université de Nantes, Laboratoire de Mathématiques Jean Leray, CNRS UMR 6629, 2 rue de la Houssinière, BP 92208, 44322 Nantes, France 
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     title = {A class of robust numerical schemes to compute front propagation},
     journal = {The SMAI Journal of computational mathematics},
     pages = {375--397},
     publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
     volume = {4},
     year = {2018},
     doi = {10.5802/smai-jcm.39},
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Therme, Nicolas. A class of robust numerical schemes to compute front propagation. The SMAI Journal of computational mathematics, Tome 4 (2018), pp. 375-397. doi: 10.5802/smai-jcm.39

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