A fast algorithm for solving first-order PDEs by L1-minimization
Guermond, Jean-Luc ; Marpeau, Fabien ; Popov, Bojan
Commun. Math. Sci., Tome 6 (2008) no. 1, p. 199-216 / Harvested from Project Euclid
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In this paper, we state a convergence result for an $L1$-based finite element approximation technique in one dimension. The proof of this result is constructive and provides the basis for an algorithm for computing $L1$-based almost minimizers with optimal complexity. Several numerical results are presented to illustrate the performance of the method.
Publié le : 2008-03-15
Classification:  finite elements,  best L1-approximation,  viscosity solution,  transport,  ill-posed problem,  HJ equation,  eikonal equation,  65N35,  65N22,  65F05,  35J05 
@article{1204905784,
     author = {Guermond, Jean-Luc and Marpeau, Fabien and Popov, Bojan},
     title = {A fast algorithm for solving first-order PDEs by L1-minimization},
     journal = {Commun. Math. Sci.},
     volume = {6},
     number = {1},
     year = {2008},
     pages = { 199-216},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1204905784}
}

Guermond, Jean-Luc; Marpeau, Fabien; Popov, Bojan. A fast algorithm for solving first-order PDEs by L1-minimization. Commun. Math. Sci., Tome 6 (2008) no. 1, pp.  199-216. http://gdmltest.u-ga.fr/item/1204905784/