We suggest a finite dfference scheme for the Camassa–Holm equation that can handle general H^1 initial data. The form of the difference scheme is judiciously chosen to ensure that it satisfies a total energy inequality. We prove that the difference scheme converges strongly in H^1 toward a dissipative weak solution of the Camassa–Holm equation.
A convergent finite difference scheme for the Camassa-Holm equation with general $H^1$ initial data / Coclite, Giuseppe Maria; Karlsen, K. H.; Risebro, N. H.. - In: SIAM JOURNAL ON NUMERICAL ANALYSIS. - ISSN 0036-1429. - 46:3(2008), pp. 1554-1579. [10.1137/060673242]
A convergent finite difference scheme for the Camassa-Holm equation with general $H^1$ initial data
COCLITE, Giuseppe Maria;
2008-01-01
Abstract
We suggest a finite dfference scheme for the Camassa–Holm equation that can handle general H^1 initial data. The form of the difference scheme is judiciously chosen to ensure that it satisfies a total energy inequality. We prove that the difference scheme converges strongly in H^1 toward a dissipative weak solution of the Camassa–Holm equation.File in questo prodotto:
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