Adaptive Gradient-Augmented Level Set Method with Multiresolution Error Estimation

Dmitry Kolomenskiy, Jean Christophe Nave, Kai Schneider

Research output: Contribution to journalArticlepeer-review

4 Citations (Scopus)


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 precision of the new fully adaptive method is analysed and speed up of CPU time and memory compression with respect to the uniform grid discretization are reported.

Original languageEnglish
Pages (from-to)116-140
Number of pages25
JournalJournal of Scientific Computing
Issue number1
Publication statusPublished - 1 Jan 2016
Externally publishedYes


  • Advection equation
  • Gradient augmented level-set method
  • Hermite multiresolution
  • Space–time adaptivity


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