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Convergence of the two-point upstream weighting scheme


Author: Marie-Claude Viallon
Journal: Math. Comp. 57 (1991), 569-584
MSC: Primary 65M12; Secondary 35L65
DOI: https://doi.org/10.1090/S0025-5718-1991-1094962-2
MathSciNet review: 1094962
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Abstract: Convergence to the entropy solution of a second-order scheme for the resolution of scalar hyperbolic conservation laws is studied. We consider the case of the so-called two-point upstream weighting scheme, widely used in petroleum engineering, to solve fluid flows in porous media problems. We prove convergence of the two-point upstream weighting scheme to the entropy solution for both discrete and semidiscrete approximations.


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DOI: https://doi.org/10.1090/S0025-5718-1991-1094962-2
Article copyright: © Copyright 1991 American Mathematical Society