Numerical conservative solutions of the Hunter--Saxton equation

Abstract

In the article a convergent numerical method for conservative solutions of the Hunter--Saxton equation is derived. The method is based on piecewise linear projections, followed by evolution along characteristics where the time step is chosen in order to prevent wave breaking. Convergence is obtained when the time step is proportional to the square root of the spatial step size, which is a milder restriction than the common CFL condition for conservation laws.

References in corpus (4)

• An integrable shallow water equation with peaked solitons
• The Kolmogorov-Riesz compactness theorem
• Existence and Lipschitz stability for $\alpha$-dissipative solutions of the two-component Hunter-Saxton system
• Stability and convergence of a conservative finite difference scheme for the modified Hunter--Saxton equation

Cited by in corpus (5)

• Uniqueness of conservative solutions for the Hunter-Saxton equation
• A Convergent Numerical Algorithm for $\alpha$-Dissipative Solutions of the Hunter-Saxton Equation
• A numerical study of variational discretizations of the Camassa-Holm equation
• A numerical view on α-dissipative solutions of the Hunter-Saxton equation
• Rate of convergence for numerical $\alpha$-dissipative solutions of the Hunter-Saxton equation