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Convergence of finite volume monotone schemes for scalar conservation laws on bounded domains. (English) Zbl 1007.65066
This paper is concerned with the study of the finite volume methods used in the discretization of scalar conservation laws with initial and boundary data as measurable bounded functions. The existence of a measure-valued solution gives rise to a weak entropy solution which allows studying the convergence of the numerical scheme associated with the continuous problem. Here, using a generalized notion of solution, similar to the one of measure-valued solution, it is deduced that the numerical solution converges to the entropy weak solution of the continuum problem.

MSC:
65M12 Stability and convergence of numerical 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
35L65 Hyperbolic conservation laws
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