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- Sylvie Champier
- 1997

In this paper, we study a nite volume approximation of a nonlinear hyperbolic equation with source term q where q is a C 1 function from IR 3 to IR, nonincreasing w.r.t. the third variable with a third derivative which is bounded. We also suppose that q(:; :; 0) 0. We suppose that u0 is in BV (IR N). We use an explicit scheme with an implicit discretization… (More)

- Claire Chainais-Hillairet, Sylvie Champier
- Numerische Mathematik
- 2001

In this paper, we study nite volume schemes for the nonhomogeneous scalar conservation law u t +divF(x; t; u) = q(x; t; u) with initial condition u(x; 0) = u 0 (x). The source term may be either stii or nonstii. In both cases, we prove error estimates between the approximate solution given by a nite volume scheme (the scheme is totally explicit in the… (More)

- S Champier, T Gallou Et, R Herbin
- 1993

We study here the discretisation of the nonlinear hyperbolic equation ut + div(vf(u)) = 0 in IR 2 IR+, with given initial condition u(:; 0) = u0(:) in IR 2 , where v is a function from IR 2 IR+ to IR 2 such that divv = 0 and f is a given nondecreasing function from IR to IR. An explicit Euler scheme is used for the time discretisation of the equation, and a… (More)

- Sylvie Champier, Laurence Grammont
- Appl. Math. Lett.
- 2001

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