Energy-preserving H1-Galerkin schemes for the Hunter--Saxton equation
Abstract
We consider the numerical integration of the Hunter--Saxton equation, which models the propagation of weakly nonlinear orientation waves. For the equation, we present two weak forms and their Galerkin discretizations. The Galerkin schemes preserve the Hamiltonian of the equation and can be implemented with cheap H1 elements. Numerical experiments confirm the effectiveness of the schemes.
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