Alternating evolution methods for static Hamilton–Jacobi equations

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Abstract

We design, analyze and numerically validate alternating evolution schemes for solving static Hamilton–Jacobi equations. This class of high resolution numerical schemes is based on the alternating evolution reformulation of the original Hamilton–Jacobi equation. Stability and convergence properties are proven for first order schemes. Numerical implementation of up to third order schemes is carried out for a set of widely used examples. Further application of the proposed method to the kinetic Hamilton–Jacobi equation is given, while the Hamiltonian is determined by an integral in phase space.

MSC

35L60
65N06
65N12

Keywords

Hamilton–Jacobi equation
Viscosity solution
Finite difference
Alternating evolution

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