An optimal L1-minimization algorithm for stationary Hamilton-Jacobi equations

Jean-Luc Guermond, Bojan Popov

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

Abstract

We describe an algorithm for solving steady one-dimensional convex-like Hamilton-Jacobi equations using a L1-minimization technique on piecewise linear approximations. For a large class of convex Hamiltonians, the algorithm is proven to be convergent and of optimal complexity whenever the viscosity solution is q-semiconcave. Numerical results are presented to illustrate the performance of the method.
Original languageEnglish (US)
Pages (from-to)211-238
Number of pages28
JournalCommunications in Mathematical Sciences
Volume7
Issue number1
DOIs
StatePublished - 2009
Externally publishedYes

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