Adaptive Filtered Schemes for First Order Hamilton-Jacobi Equations

  • Maurizio Falcone
  • Giulio PaolucciEmail author
  • Silvia Tozza
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 126)


In this paper we consider a class of “filtered” schemes for some first order time dependent Hamilton-Jacobi equations. A typical feature of a filtered scheme is that at the node xj the scheme is obtained as a mixture of a high-order scheme and a monotone scheme according to a filter function F. The mixture is usually governed by F and by a fixed parameter ε = ε(Δt, Δx) > 0 which goes to 0 as (Δt, Δx) is going to 0 and does not depend on n. Here we improve the standard filtered scheme introducing an adaptive and automatic choice of the parameter ε = εn(Δt, Δx) at every iteration. To this end, we use a smoothness indicator in order to select the regions where we can compute the regularity threshold εn. The numerical tests presented confirms the effectiveness of the adaptive scheme.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Maurizio Falcone
    • 1
  • Giulio Paolucci
    • 1
    Email author
  • Silvia Tozza
    • 2
  1. 1.Department of MathematicsSapienza University of RomeRomeItaly
  2. 2.Istituto Nazionale di Alta Matematica/Department of MathematicsSapienza University of RomeRomeItaly

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