More on stochastic and variational approach to the Lax-Friedrichs scheme
A stochastic and variational aspect of the Lax-Friedrichs scheme applied to hyperbolic scalar conservation laws and Hamilton-Jacobi equations generated by space-time dependent flux functions of the Tonelli type was clarified by Soga (2015). The results for the Lax-Friedrichs scheme are extended here...
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| Veröffentlicht in: | Mathematics of computation 2016-09, Vol.85 (301), p.2161-2193 |
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| container_title | Mathematics of computation |
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| creator | Soga, Kohei |
| description | A stochastic and variational aspect of the Lax-Friedrichs scheme applied to hyperbolic scalar conservation laws and Hamilton-Jacobi equations generated by space-time dependent flux functions of the Tonelli type was clarified by Soga (2015). The results for the Lax-Friedrichs scheme are extended here to show its time-global stability, the large-time behavior, and error estimates. Also provided is a weak KAM-like theorem for discrete equations that is useful in the numerical analysis and simulation of the weak KAM theory. As one application, a finite difference approximation to effective Hamiltonians and KAM tori is rigorously treated. The proofs essentially rely on the calculus of variations in the Lax-Friedrichs scheme and on the theory of viscosity solutions of Hamilton-Jacobi equations. |
| doi_str_mv | 10.1090/mcom/3061 |
| format | Article |
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| source | American Mathematical Society Publications (Freely Accessible); JSTOR Mathematics & Statistics; Jstor Complete Legacy; American Mathematical Society Publications |
| title | More on stochastic and variational approach to the Lax-Friedrichs scheme |
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