HOMOGENIZATION OF HAMILTON–JACOBI EQUATIONS: NUMERICAL METHODS

DOI10.1142/S0218202508002978zbMath1155.65072MaRDI QIDQ3529193

Fabio Camilli, Yves Achdou, Italo Capuzzo-Dolcetta

Publication date: 20 October 2008

Published in: Mathematical Models and Methods in Applied Sciences (Search for Journal in Brave)

zbMATH Keywords

error estimatesHamilton-Jacobi equationviscosity solutionhomogenization

Mathematics Subject Classification ID

Nonlinear first-order PDEs (35F20) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25) Homogenization in context of PDEs; PDEs in media with periodic structure (35B27)

Related Items (11)

Discontinuous Galerkin and C⁰-IP finite element approximation of periodic Hamilton–Jacobi–Bellman–Isaacs problems with application to numerical homogenization ⋮ Error estimates for approximation schemes of effective Hamiltonians arising in stochastic homogenization of Hamilton-Jacobi equations ⋮ Error analysis of the high order scheme for homogenization of Hamilton-Jacobi equation ⋮ A Simple Explicit Operator-Splitting Method for Effective Hamiltonians ⋮ A posteriori error estimates for the effective Hamiltonian of dislocation dynamics ⋮ Homogenization and Vanishing Viscosity in Fully Nonlinear Elliptic Equations: Rate of Convergence Estimates ⋮ Min-max formulas and other properties of certain classes of nonconvex effective Hamiltonians ⋮ HOMOGENIZATION OF FIRST-ORDER EQUATIONS WITH u/∊-PERIODIC HAMILTONIAN: RATE OF CONVERGENCE AS ∊ → 0 AND NUMERICAL METHODS ⋮ A Generalized Newton Method for Homogenization of Hamilton--Jacobi Equations ⋮ Mixed Finite Element Approximation of Periodic Hamilton--Jacobi--Bellman Problems With Application to Numerical Homogenization ⋮ Approximation of optimal control surfaces for \(2\times 2\) skew-symmetric evolutionary game dynamics

Cites Work

• Unnamed Item
• Approximate solutions of the Bellman equation of deterministic control theory
• Fronts propagating with curvature-dependent speed: Algorithms based on Hamilton-Jacobi formulations
• Lagrangian graphs, minimizing measures and Mañé's critical values
• Singular perturbations of nonlinear degenerate parabolic pDEs: A general convergence result
• Semi-Lagrangian schemes for Hamilton-Jacobi equations, discrete representation formulae and Godunov methods
• An approximation scheme for the effective Hamiltonian and applications
• Convergence of numerical methods and parameter dependence of min-plus eigenvalue problems, Frenkel-Kontorova models and homogenization of Hamilton-Jacobi equations
• Two approximations of solutions of Hamilton-Jacobi equations
• Homogenization of a Hamilton–Jacobi equation associated with the geometric motion of an interface
• Computing the Effective Hamiltonian Using a Variational Approach
• Large scale front dynamics for turbulent reaction-diffusion equations with separated velocity scales

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