$L^1$-Approximation of Stationary HamiltonJacobi Equations Academic Article uri icon

abstract

  • We describe a nonlincar finite element technique to approximate the solutions of stationary Hamilton-Jacobi equations in two space dimcnsions using continuous finite elements of arbitrary degree. The method consists of minimizing a functional containing the L1-norm of the Hamiltonian plus a discrete entropy. It is shown that the approximatc sequence converges to the unique viscosity solution under appropriate hypotheses on the Hamiltonian and the mesh family. © 2008 Society for Industrial and Applied Mathematics.

author list (cited authors)

  • Guermond, J., & Popov, B.

publication date

  • January 1, 2008 11:11 AM