Communications in Mathematical Sciences

Volume 7 (2009)

Number 1

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

Pages: 211 – 238



Jean-Luc Guermond

Bojan Popov


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.


Finite elements, best L1-approximation, viscosity solution, HJ equation, eikonal equation

2010 Mathematics Subject Classification

35J05, 65F05, 65N22, 65N35

Published 1 January 2009