Monotone first-order weighted schemes for scalar conservation laws

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Abstract

In this work, we present a monotone first-order weighted (FORWE) method for scalar conservation laws using a variational formulation. We prove theoretical properties as consistency, monotonicity, and convergence of the proposed scheme for the one-dimensional (1D) Cauchy problem. These convergence results are extended to multidimensional scalar conservation laws by a dimensional splitting technique. For the validation of the FORWE method, we consider some standard bench-mark tests of bidimensional and 1D conservation law equations. Finally, we analyze the accuracy of the method with L1 and L error estimates. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013

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