Communications in Mathematical Sciences

Volume 6 (2008)

Number 1

A fast algorithm for solving first-order PDEs by L1-minimization

Pages: 199 – 216



Jean-Luc Guermond

Fabien Marpeau

Bojan Popov


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.


finite elements; best L1-approximation; viscosity solution; transport; ill-posed problem; HJ equation; eikonal equation

2010 Mathematics Subject Classification

35J05, 65F05, 65N22, 65N35

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