Sylvie Champier

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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)
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)
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)
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