We present a novel approach to determine the evolution of level sets under uncertainties in the velocity fields. This leads to a stochastic description of the level sets. To compute the quantiles of random level sets, we use the stochastic Galerkin method for a hyperbolic reformulation of the level-set equations. A novel intrusive Galerkin formulation is presented and proven hyperbolic. It induces a corresponding finite-volume scheme that is specifically taylored for uncertain velocities.

翻译：我们提出了一个新颖的方法来确定在速度字段不确定情况下的等级设置的演变。 这导致对等级设置进行随机描述。 为了计算随机等级组的量化, 我们使用随机等级组的振荡加勒金法来重拟等级设置方程的双曲。 我们展示了一种新型的侵扰性加勒金配方, 并证明了它具有双曲性。 它引出一种相应的有限量方案, 具体地说, 用于不确定速度的微量方案 。