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Convergence of finite volume schemes for triangular systems of conservation laws

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Abstract

We consider non-strictly hyperbolic systems of conservation laws in triangular form, which arise in applications like three-phase flows in porous media. We device simple and efficient finite volume schemes of Godunov type for these systems that exploit the triangular structure. We prove that the finite volume schemes converge to weak solutions as the discretization parameters tend to zero. Some numerical examples are presented, one of which is related to flows in porous media.

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Correspondence to Kenneth Hvistendahl Karlsen.

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The research of K. H. Karlsen was supported by an Outstanding Young Investigators Award from the Research Council of Norway.

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Karlsen, K.H., Mishra, S. & Risebro, N.H. Convergence of finite volume schemes for triangular systems of conservation laws. Numer. Math. 111, 559–589 (2009). https://doi.org/10.1007/s00211-008-0199-x

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