Journal
SIAM JOURNAL ON NUMERICAL ANALYSIS
Volume 46, Issue 3, Pages 1554-1579Publisher
SIAM PUBLICATIONS
DOI: 10.1137/060673242
Keywords
camassa-Holm equation; hyperbolic-elliptic system; weak solution; finite difference scheme; convergence
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We suggest a finite difference 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 towards a dissipative weak solution of the Camassa-Holm equation.
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