Convergence of an upstream finite volume scheme for a nonlinear hyperbolic equation on a triangular mesh. (English) Zbl 0801.65089

Champier, S.; Gallouët, T.; Herbin, R.

Numer. Math. 66, No. 2, 139-157 (1993).

The following nonlinear hyperbolic problem in two-dimensional space is considered (1) \(u_ t (x,t) + \text{div} (v(x,t) f(u(x,t))) = 0\), \(x \in \mathbb{R}^ 2\), \(t \in\mathbb{R}_ +\), \(\text{div} v(x,t) = 0\), \(\sup_{x,t} | v(x,t) | < \infty\). An explicit Euler scheme is used for the time discretization of (1) and a triangular mesh for the spatial discretization. Under a usual stability condition,the convergence of the solution obtained by an upstream finite volume scheme towards the unique entropy weak solution of (1) is proved.

Reviewer: K.Zlateva (Russe)

MSC:

65M12	Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65M60	Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65M06	Finite difference methods for initial value and initial-boundary value problems involving PDEs
35L60	First-order nonlinear hyperbolic equations

Keywords:

nonlinear hyperbolic problem; explicit Euler scheme; stability; convergence; upstream finite volume scheme; entropy weak solution

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