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.

中文翻译：

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Hunter-Saxton 方程的数值保守解

在文章中，导出了亨特-萨克斯顿方程保守解的收敛数值方法。该方法基于分段线性投影，然后沿特征演化，其中选择时间步长以防止波浪破碎。当时间步长与空间步长的平方根成正比时，会获得收敛，这是比守恒定律的常见 CFL 条件更温和的限制。