A class of robust numerical schemes to compute front propagation
The SMAI journal of computational mathematics, Volume 4 (2018) , pp. 375-397.

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.

Published online: 2018-11-19
DOI: https://doi.org/10.5802/smai-jcm.39
Classification: 35F21,  65N08,  65N12
Keywords: Finite volumes, Hamilton-Jacobi, Stability, Convergence
@article{SMAI-JCM_2018__4__375_0,
     author = {Nicolas Therme},
     title = {A class of robust numerical schemes to compute front propagation},
     journal = {The SMAI journal of computational mathematics},
     publisher = {Soci\'et\'e de Math\'ematiques Appliqu\'ees et Industrielles},
     volume = {4},
     year = {2018},
     pages = {375-397},
     doi = {10.5802/smai-jcm.39},
     language = {en},
     url={smai-jcm.centre-mersenne.org/item/SMAI-JCM_2018__4__375_0/}
}
Therme, Nicolas. A class of robust numerical schemes to compute front propagation. The SMAI journal of computational mathematics, Volume 4 (2018) , pp. 375-397. doi : 10.5802/smai-jcm.39. https://smai-jcm.centre-mersenne.org/item/SMAI-JCM_2018__4__375_0/

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