Energy-preserving $H^1$-Galerkin schemes for the Hunter--Saxton equation

Geonsik Eom; Shao-Liang Zhang; Tomohiro Sogabe; Yuto Miyatake

arxiv: 1610.09918 · v1 · pith:MEA66HFWnew · submitted 2016-10-31 · 🧮 math.NA

Energy-preserving H¹-Galerkin schemes for the Hunter--Saxton equation

Yuto Miyatake , Geonsik Eom , Tomohiro Sogabe , Shao-Liang Zhang This is my paper

classification 🧮 math.NA

keywords equationgalerkinschemeshunter--saxtonnumericalcheapconfirmconsider

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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 $H^1$ elements. Numerical experiments confirm the effectiveness of the schemes.

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Energy-preserving H¹-Galerkin schemes for the Hunter--Saxton equation

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