Showing papers by "Steinar Evje published in 2003"
TL;DR: Results from test cases show that the aim of this paper is to construct hybrid FVS/FDS schemes which properly combine the accuracy of FDS in the resolution of sharp mass fronts and the robustness of FVS which ensures stability under stiff conditions.
119 citations
TL;DR: Advection Upstream Splitting Method (AUSM) schemes for hyperbolic systems of conservation laws which do not allow any analytical calculation of the Jacobian are studied in this article.
60 citations
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TL;DR: In this article, the authors present a direct proof of an L 1 error estimate for viscous approximate solutions of the initial value problem for the uniformly parabolic equation, where V is a vector field and f is a scalar function.
Abstract: Relying on recent advances in the theory of entropy solutions for nonlinear (strongly) degenerate parabolic equations, we present a direct proof of an L^1 error estimate for viscous approximate solutions of the initial value problem for \partial_t w+\mathrm{div} \bigl(V(x)f(w)\bigr)= \Delta A(w) where V=V(x) is a vector field, f=f(u) is a scalar function, and A'(.) \geq 0. The viscous approximate solutions are weak solutions of the initial value problem for the uniformly parabolic equation \partial_t w^{\epsilon}+\mathrm{div} \bigl(V(x) f(w^{\epsilon})\bigr) \Delta \bigl(A(w^{\epsilon})+\epsilon w^{\epsilon}\bigr), \epsilon>0. The error estimate is of order \sqrt{\epsilon}.
9 citations