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Convergence of an explicit finite volume scheme for first order symmetric systems. (English) Zbl 1030.65110
The aim of this paper is to derive an $$o(h^{1/2})$$ error estimate for classical upwind, explicit in time, finite volume scheme for linear first order symmetric systems under very general assumptions on the mesh and minimal regularity hypothesis on the continuous solution. The authors propose a new technique, which takes advantage of the linearity of the problem.

##### MSC:
 65N12 Stability and convergence of numerical methods for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 35F15 Boundary value problems for linear first-order PDEs
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