Open Access
March 2009 An optimal L1-minimization algorithm for stationary Hamilton-Jacobi equations
Jean-Luc Guermond, Bojan Popov
Commun. Math. Sci. 7(1): 211-238 (March 2009).


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.


Download Citation

Jean-Luc Guermond. Bojan Popov. "An optimal L1-minimization algorithm for stationary Hamilton-Jacobi equations." Commun. Math. Sci. 7 (1) 211 - 238, March 2009.


Published: March 2009
First available in Project Euclid: 27 March 2009

zbMATH: 1175.65135
MathSciNet: MR2512842

Primary: 35J05 , 65F05 , 65N22 , 65N35

Keywords: best L1-approximation , eikonal equation , finite elements , HJ equation , viscosity solution

Rights: Copyright © 2009 International Press of Boston

Vol.7 • No. 1 • March 2009
Back to Top