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L1-APPROXIMATION OF STATIONARY HAMILTON–JACOBI EQUATIONS

JEAN-LUC GUERMOND and BOJAN POPOV
SIAM Journal on Numerical Analysis
Vol. 47, No. 1 (2008/2009), pp. 339-362
Stable URL: http://www.jstor.org/stable/25663127
Page Count: 24
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L1-APPROXIMATION OF STATIONARY HAMILTON–JACOBI EQUATIONS
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Abstract

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.

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