Surface Reconstruction and Image Enhancement via $L^1$-Minimization
SIAM Journal on Scientific Computing
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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 $L^1$-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.