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Convergence results for an inhomogeneous system arising in various high frequency approximations
James, Francois ; Gosse, Laurent
HAL, hal-00079237 / Harvested from HAL
Text on HAL
This paper is devoted to both theoretical and numerical study of a system involving an eikonal equation of Hamilton-Jacobi type and a linear conservation law as it comes out of the geometrical optics expansion of the wave equation or the semiclassical limit for the Schrödinger equation. We first state an existence and uniqueness result in the framework of viscosity and duality solutions. Then we study the behavior of some classical numerical schemes on this problem and we give sufficient conditions to ensure convergence. As an illustration, some practical computations are provided.
Publié le : 2002-07-05
Classification:  Eikonal equation,  Hamilton-Jacobi equation,  linear conservation equation,  discontinuous coefficients,  viscosity solutions,  duality solutions,  finite difference schemes,  geometrical optics,  65M06;65M12,  [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP],  [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] 
@article{hal-00079237,
     author = {James, Francois and Gosse, Laurent},
     title = {Convergence results for an inhomogeneous system arising in various high frequency approximations},
     journal = {HAL},
     volume = {2002},
     number = {0},
     year = {2002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00079237}
}

James, Francois; Gosse, Laurent. Convergence results for an inhomogeneous system arising in various high frequency approximations. HAL, Tome 2002 (2002) no. 0, . http://gdmltest.u-ga.fr/item/hal-00079237/