L-approximation of Stationary Hamilton–jacobi Equations∗
نویسنده
چکیده
We describe a nonlinear finite element technique to approximate the solutions of stationary Hamilton–Jacobi equations in two space dimensions 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 approximate sequence converges to the unique viscosity solution under appropriate hypotheses on the Hamiltonian and the mesh family.
منابع مشابه
L1-Approximation of Stationary Hamilton-Jacobi Equations
We describe a nonlinear finite element technique to approximate the solutions of stationary Hamilton-Jacobi equations in two space dimensions using continuous finite elements of arbitrary degree. The method consists of minimizing a functional containing the L-norm of the Hamiltonian plus a discrete entropy. It is shown that the approximate sequence converges to the unique viscosity solution und...
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[1] J.-L. Guermond and B. Popov, Linear advection with ill-posed boundary conditions via L1-minimization, Numerical Analysis and Modeling 4 (2007), 39–47. [2] J.-L. Guermond and B. Popov, L1-minimization methods for Hamilton-Jacobi equations: the one-dimensional case, submitted. [3] J.-L. Guermond and B. Popov, L1-approximation of stationary Hamilton-Jacobi equations, submitted. [4] J.-L. Guerm...
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