Adaptive gradient-augmented level set method with multiresolution error estimation

@article{Kolomenskiy2016AdaptiveGL,
  title={Adaptive gradient-augmented level set method with multiresolution error estimation},
  author={Dmitry Kolomenskiy and Jean-Christophe Nave and Kai Schneider},
  journal={J. Sci. Comput.},
  year={2016},
  volume={66},
  pages={116-140}
}
A space–time adaptive scheme is presented for solving advection equations in two space dimensions. The gradient-augmented level set method using a semi-Lagrangian formulation with backward time integration is coupled with a point value multiresolution analysis using Hermite interpolation. Thus locally refined dyadic spatial grids are introduced which are efficiently implemented with dynamic quadtree data structures. For adaptive time integration, an embedded Runge–Kutta method is employed. The… CONTINUE READING
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