Energy-preserving H1-Galerkin schemes for shallow water wave equations with peakon solutions
Y Miyatake, T Matsuo - Physics Letters A, 2012 - Elsevier
New energy-preserving Galerkin schemes for the Camassa–Holm and the Degasperis–
Procesi equations which model shallow water waves are presented. The schemes can be
implemented only with cheap H1 elements, which is expected to be sufficient to catch the
characteristic peakon solutions. The keys of the derivation are the Hamiltonian structures of
the equations and an L2-projection technique newly employed in the present Letter to mimic
the Hamiltonian structures in a discrete setting, so that the desired energy-preserving …
Procesi equations which model shallow water waves are presented. The schemes can be
implemented only with cheap H1 elements, which is expected to be sufficient to catch the
characteristic peakon solutions. The keys of the derivation are the Hamiltonian structures of
the equations and an L2-projection technique newly employed in the present Letter to mimic
the Hamiltonian structures in a discrete setting, so that the desired energy-preserving …
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