Numerical conservative solutions of the Hunter–Saxton equation
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We derive a convergent (up to a subsequence) numerical method for conservative solutions of the Hunter–Saxton equation. 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. We find that the constraint Δ t ≤ C √(Δ x ) is sufficient, which is a milder restriction than the common CFL condition for conservation laws.
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