$L^1$-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.

published proceedings

  • SIAM Journal on Numerical Analysis

author list (cited authors)

  • Guermond, J., & Popov, B.

citation count

  • 8

complete list of authors

  • Guermond, Jean-Luc||Popov, Bojan

publication date

  • January 2009