L1-minimization methods for Hamilton–Jacobi equations: the one-dimensional case

Authors:
Jean-Luc Guermond;Bojan Popov
Affiliations:
Texas A&M University, Department of Mathematics, 3368 TAMU, 77843, College Station, TX, USA;Texas A&M University, Department of Mathematics, 3368 TAMU, 77843, College Station, TX, USA
Venue:
Numerische Mathematik
Year:
2008

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Abstract

A new approximation technique based on L 1-minimization is introduced. It is proven that the approximate solution converges to the viscosity solution in the case of one-dimensional stationary Hamilton–Jacobi equation with convex Hamiltonian.