Numerical approximations of one-dimensional linear conservation equations with discontinuous coefficients
Gosse, Laurent ; James, Francois
HAL, hal-00419729 / Harvested from HAL
Text on HAL
Conservative linear equations arise in many areas of application, including continuum mechanics or high-frequency geometrical optics approximations. This kind of equations admits most of the time solutions which are only bounded measures in the space variable known as duality solutions. In this paper, we study the convergence of a class of finite-differences numerical schemes and introduce an appropriate concept of consistency with the continuous problem. Some basic examples including computational results are also supplied.
Publié le : 2000-07-05
Classification:  Linear conservation equations,  duality solutions,  finite difference schemes,  weak consistency,  nonconservative product,  65M06; 65M12; 35F10,  [MATH.MATH-NA]Mathematics [math]/Numerical Analysis [math.NA] 
@article{hal-00419729,
     author = {Gosse, Laurent and James, Francois},
     title = {Numerical approximations of one-dimensional linear conservation equations with discontinuous coefficients},
     journal = {HAL},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00419729}
}

Gosse, Laurent; James, Francois. Numerical approximations of one-dimensional linear conservation equations with discontinuous coefficients. HAL, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/hal-00419729/