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March 2008 A fast algorithm for solving first-order PDEs by L1-minimization
Jean-Luc Guermond, Fabien Marpeau, Bojan Popov
Commun. Math. Sci. 6(1): 199-216 (March 2008).


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.


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Jean-Luc Guermond. Fabien Marpeau. Bojan Popov. "A fast algorithm for solving first-order PDEs by L1-minimization." Commun. Math. Sci. 6 (1) 199 - 216, March 2008.


Published: March 2008
First available in Project Euclid: 7 March 2008

zbMATH: 1143.65060
MathSciNet: MR2398004

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

Keywords: best L1-approximation , eikonal equation , finite elements , HJ equation , Ill-posed problem , transport , viscosity solution

Rights: Copyright © 2008 International Press of Boston

Vol.6 • No. 1 • March 2008
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