More on stochastic and variational approach to the Lax-Friedrichs scheme

DOI10.1090/mcom/3061zbMath1342.65176arXiv1210.2178OpenAlexW2962974943MaRDI QIDQ2814435

Kohei Soga

Publication date: 22 June 2016

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1210.2178

zbMATH Keywords

stabilityHamilton-Jacobi equationinitial value problemerror estimatecalculus of variationsrandom walkLax-Friedrichs schemeweak KAM theoryscalar conservation law

Mathematics Subject Classification ID

Hyperbolic conservation laws (35L65) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Perturbations, KAM theory for infinite-dimensional Hamiltonian and Lagrangian systems (37K55) Hamilton-Jacobi equations (35F21)

Related Items (5)

Weak KAM theory for discounted Hamilton-Jacobi equations and its application ⋮ Filling times for linear flow on the torus with truncated Diophantine conditions: a brief review and new proof ⋮ Selection problems of \({{\mathbb {Z}}}^2\)-periodic entropy solutions and viscosity solutions ⋮ Weak KAM theory for action minimizing random walks ⋮ Stochastic and variational approach to finite difference approximation of Hamilton-Jacobi equations

Cites Work

• Unnamed Item
• Semiconcave functions, Hamilton-Jacobi equations, and optimal control
• Action minimizing invariant measures for positive definite Lagrangian systems
• Ergodization rates for linear flow on the torus
• On the distribution of free path lengths for the periodic Lorentz gas
• Aubry-Mather theory and Hamilton-Jacobi equations
• KAM-stable Hamiltonians
• Space-time continuous limit of random walks with hyperbolic scaling
• The Cauchy problem for a nonlinear first order partial differential equation
• Difference approximation to Aubry–Mather sets of the forced Burgers equation
• The Large-Time Behavior of the Scalar, Genuinely Nonlinear Lax-Friedrichs Scheme
• Recent Developments in the Theory of Hamiltonian Systems
• Aubry-Mather theory and periodic solutions of the forced Burgers equation
• Monotone Difference Approximations for Scalar Conservation Laws
• Accuracy of some approximate methods for computing the weak solutions of a first-order quasi-linear equation
• Théorème KAM faible et théorie de Mather sur les systèmes lagrangiens
• The Optimal Convergence Rate of Monotone Finite Difference Methods for Hyperbolic Conservation Laws
• The asymptotic behaviour of solutions of the forced Burgers equation on the circle
• Minimizing Measures for Time-Dependent Lagrangians
• A numerically accessible criterion for the breakdown of quasi-periodic solutions and its rigorous justification
• Discontinuous solutions of non-linear differential equations
• Stochastic and variational approach to the Lax-Friedrichs scheme

This page was built for publication: More on stochastic and variational approach to the Lax-Friedrichs scheme