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

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.


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
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