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Monotone first‐order weighted schemes for scalar conservation laws
Author(s) -
Jerez Silvia
Publication year - 2013
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.21796
Subject(s) - conservation law , mathematics , scalar (mathematics) , monotone polygon , monotonic function , convergence (economics) , consistency (knowledge bases) , order (exchange) , law , mathematical analysis , discrete mathematics , geometry , political science , economics , economic growth , finance
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 L 1 and L ∞ error estimates. © 2013 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013