An optimal \(L_1\)-minimization algorithm for stationary Hamilton-Jacobi equations. (English) Zbl 1175.65135

Guermond, Jean-Luc; Popov, Bojan

Commun. Math. Sci. 7, No. 1, 211-238 (2009).

The authors construct a sequence of approximate solutions to some one-dimensional stationary Hamilton-Jacobi equations by using continuous finite elements and by minimizing the residual in the Lebesgue space with \(p=1\). For a class of convex Hamiltonians, they prove the convergence of the proposed algorithm. Some numerical examples are carried out.

Reviewer: Calin Ioan Gheorghiu (Cluj-Napoca)

MSC:

65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35F21	Hamilton-Jacobi equations
49L25	Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
65N12	Stability and convergence of numerical methods for boundary value problems involving PDEs

Keywords:

finite element method; best approximation; viscosity solutions; eikonal equation; Hamilton-Jacobi equations; algorithm; numerical examples