L-1-APPROXIMATION OF STATIONARY HAMILTON-JACOBI EQUATIONS Academic Article

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.

authors

• Popov, Bojan

published proceedings

• SIAM JOURNAL ON NUMERICAL ANALYSIS

author list (cited authors)

• Guermond, J., & Popov, B.

citation count

• 9

complete list of authors

• Guermond, Jean-Luc||Popov, Bojan

publication date

• January 2008

publisher

• Society for Industrial & Applied Mathematics (SIAM)  Publisher

published in

• SIAM Journal on Numerical Analysis  Journal

keywords

• Best L-1-approximation
• Finite Elements
• Hamilton-jacobi Equations
• Viscosity Solution

Digital Object Identifier (DOI)

• 10.1137/070681922

URI

• https://hdl.handle.net/1969.1/185461

start page

• 339

end page

• 362

volume

• 47

issue

• 1

URL

• http://dx.doi.org/10.1137/070681922