On long time error bounds for the wave equation on second order form

DOI10.1007/s10915-018-0667-0zbMath1405.65099OpenAlexW2582356345MaRDI QIDQ1785490

Jan Nordström, Hannes Frenander

Publication date: 28 September 2018

Published in: Journal of Scientific Computing (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10915-018-0667-0

zbMATH Keywords

wave equationtemporal error bounds

Mathematics Subject Classification ID

Wave equation (35L05) 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)

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A new variational discretization technique for initial value problems bypassing governing equations ⋮ A comparative study of two different shallow water formulations using stable summation by parts schemes ⋮ An energy stable coupling procedure for the compressible and incompressible Navier-Stokes equations ⋮ On the convergence rates of energy-stable finite-difference schemes ⋮ Numerical Solution of 3D Exterior Unsteady Wave Propagation Problems Using Boundary Operators ⋮ Accuracy of stable, high-order finite difference methods for hyperbolic systems with non-smooth wave speeds ⋮ The spatial operator in the incompressible Navier-Stokes, Oseen and Stokes equations

Cites Work

• Review of summation-by-parts schemes for initial-boundary-value problems
• Stable boundary treatment for the wave equation on second-order form
• Convergence of summation-by-parts finite difference methods for the wave equation
• Summation by parts operators for finite difference approximations of second derivatives
• Error boundedness of discontinuous Galerkin spectral element approximations of hyperbolic problems
• Summation-By-Parts in Time: The Second Derivative
• Error Bounded Schemes for Time-dependent Hyperbolic Problems
• Difference Approximations for the Second Order Wave Equation
• On error bounds of finite difference approximations to partial differential equations. -- Temporal behavior and rate of convergence

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