Katrin Grunert

collaborators

3 papers

math.NA2025

Rate of convergence for numerical $I^\pm$ -dissipative solutions of the Hunter-Saxton equation

Thomas Christiansen, Katrin Grunert

We prove that $I^\pm$ -dissipative solutions to the Cauchy problem of the Hunter-Saxton equation, where $I^\pm \in W^{1, \infty} (R, [0, 1))$ , can be computed numerically with orde…

math.AP2025

Wave breaking for the nonlinear variational wave equation

Sondre Tesdal Galtung, Katrin Grunert

Following conservative solutions of the nonlinear variational wave equation $u_{tt} - c (u) (c (u) u_{x})_{x} = 0$ along forward and backward characteristics, we identify criteria, which guara…

math.NA2024

A numerical view on Î±-dissipative solutions of the Hunter-Saxton equation

Thomas Christiansen, Katrin Grunert

We propose a new numerical method for $I^\pm$ -dissipative solutions of the Hunter-Saxton equation, where $I^\pm$ belongs to $W^{1, \infty} (R, [0, 1))$ . The method combines a pro…

Rate of convergence for numerical I^±-dissipative solutions of the Hunter-Saxton equation

Wave breaking for the nonlinear variational wave equation

A numerical view on Î±-dissipative solutions of the Hunter-Saxton equation

Rate of convergence for numerical $I^\pm$ -dissipative solutions of the Hunter-Saxton equation