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Error estimates for approximation schemes of effective Hamiltonians arising in stochastic homogenization of Hamilton-Jacobi equations. (English) Zbl 1366.65082

The paper deals with a numerical scheme for effective Hamiltonians which arises in the homogenization of first-order Hamilton-Jacobi equations in stationary ergodic settings. This work is motivated by front propagation problems, but the results that we obtain here can be generalized to other types of Hamiltonians. The author presents a finite volume scheme for the efective Hamiltonian and proves error estimates concerning the rate of convergence of the approximated solution to the exact one. No numerical examples are presented.

MSC:

65M15 Error bounds for initial value and initial-boundary value problems involving PDEs
35F21 Hamilton-Jacobi equations
35B27 Homogenization in context of PDEs; PDEs in media with periodic structure
49L25 Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games
65M08 Finite volume methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
65P10 Numerical methods for Hamiltonian systems including symplectic integrators
37H10 Generation, random and stochastic difference and differential equations
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