BV estimates of Lax-Friedrichs' scheme for a class of nonlinear hyperbolic conservation laws |
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| Authors: | Tong Yang Huijiang Zhao Changjiang Zhu |
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| Institution: | Department of Mathematics, City University of Hong Kong, Hong Kong ; Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences, Wuhan, People's Republic of China ; Laboratory of Nonlinear Analysis and Department of Mathematics, Central China Normal University, Wuhan, People's Republic of China |
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| Abstract: | We give uniform BV estimates and  -stability of Lax-Friedrichs' scheme for a class of  systems of strictly hyperbolic conservation laws whose integral curves of the eigenvector fields are straight lines, i.e., Temple class, under the assumption of small total variation. This implies that the approximate solutions generated via the Lax-Friedrichs' scheme converge to the solution given by the method of vanishing viscosity or the Godunov scheme, and then the Glimm scheme or the wave front tracking method. |
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| Keywords: | Hyperbolic systems of conservation laws Lax-Friedrichs' scheme BV estimates |
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