An adaptive method with rigorous error control for the Hamilton-Jacobi equations. I: The one-dimensional steady state case

DOI10.1016/j.apnum.2004.08.030zbMath1063.65078OpenAlexW2071602743MaRDI QIDQ1765345

Bernardo Cockburn, Bayram Yenikaya

Publication date: 23 February 2005

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2004.08.030

zbMATH Keywords

Hamilton-Jacobi equationsConvergenceA posteriori error estimatesNumerical examplesAdaptivityError controlViscosity solution

Mathematics Subject Classification ID

First-order nonlinear hyperbolic equations (35L60) 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) Viscosity solutions to Hamilton-Jacobi equations in optimal control and differential games (49L25)

Related Items (7)

Fifth-order weighted power-ENO schemes for Hamilton-Jacobi equations ⋮ Essentially non-oscillatory adaptive tree methods ⋮ An adaptive high-order discontinuous Galerkin method with error control for the Hamilton-Jacobi equations. I: The one-dimensional steady state case ⋮ Local a posteriori error estimates for time-dependent Hamilton-Jacobi equations ⋮ Three-dimensional data transfer operators in large plasticity deformations using modified-SPR technique ⋮ An adaptive method with rigorous error control for the Hamilton--Jacobi equations. II: The two-dimensional steady-state case ⋮ Adaptive spline interpolation for Hamilton-Jacobi-Bellman equations

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