Summary.
In this paper, we study finite volume schemes for the nonhomogeneous scalar conservation law \(u_t +{\rm div} F(x,t,u)=q(x,t,u)\) with initial condition \(u(x,0)=\u0(x)\). The source term may be either stiff or nonstiff. In both cases, we prove error estimates between the approximate solution given by a finite volume scheme (the scheme is totally explicit in the nonstiff case, semi-implicit in the stiff case) and the entropy solution. The order of these estimates is \(h^{\frac{1}{4}}\) in space-time \(L^1\)-norm (h denotes the size of the mesh). Furthermore, the error estimate does not depend on the stiffness of the source term in the stiff case.
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Received October 21, 1999 / Published online February 5, 2001
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Chainais-Hillairet, C., Champier, S. Finite volume schemes for nonhomogeneous scalar conservation laws: error estimate. Numer. Math. 88, 607–639 (2001). https://doi.org/10.1007/PL00005452
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DOI: https://doi.org/10.1007/PL00005452