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Error estimates for approximation schemes of effective Hamiltonians arising in stochastic homogenization of Hamilton-Jacobi equations

Hajej, Ahmed (2016), Error estimates for approximation schemes of effective Hamiltonians arising in stochastic homogenization of Hamilton-Jacobi equations, Numerical Algorithms, 73, 3, p. 839-868. 10.1007/s11075-016-0120-0

Type
Article accepté pour publication ou publié
Date
2016
Journal name
Numerical Algorithms
Volume
73
Number
3
Publisher
Baltzer
Pages
839-868
Publication identifier
Metadata
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Author(s)
Hajej, Ahmed
Abstract (EN)
We study approximation schemes for effective Hamiltonians arising in the homogenization of first order Hamilton-Jacobi equations in stationary ergodic settings. In particular, we prove error estimates concerning the rate of convergence of the approximated solution to the effective Hamiltonian. Our main motivations are front propagation problems, but our results can be generalized to other types of Hamiltonians.
Subjects / Keywords
Hamilton-Jacobi equation; Front propagation; Homogenization in random media; Homogenization in periodic media; Effective Hamiltonian; Error estimate; Viscosity solution