An optimal L1-minimization algorithm for stationary Hamilton-Jacobi equations
Guermond, Jean-Luc ; Popov, Bojan
Commun. Math. Sci., Tome 7 (2009) no. 1, p. 211-238 / Harvested from Project Euclid
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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.
Publié le : 2009-03-15
Classification:  Finite elements,  best L1-approximation,  viscosity solution,  HJ equation,  eikonal equation,  65N35,  65N22,  65F05,  35J05 
@article{1238158613,
     author = {Guermond, Jean-Luc and Popov, Bojan},
     title = {An optimal L1-minimization algorithm for stationary Hamilton-Jacobi equations},
     journal = {Commun. Math. Sci.},
     volume = {7},
     number = {1},
     year = {2009},
     pages = { 211-238},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1238158613}
}

Guermond, Jean-Luc; Popov, Bojan. An optimal L1-minimization algorithm for stationary Hamilton-Jacobi equations. Commun. Math. Sci., Tome 7 (2009) no. 1, pp.  211-238. http://gdmltest.u-ga.fr/item/1238158613/