Adjoint recovery of superconvergent linear functionals from Galerkin approximations. The one-dimensional case

DOI10.1007/S10915-007-9129-9zbMath1134.65052OpenAlexW1979161420MaRDI QIDQ2385511

Ryuhei Ichikawa, Bernardo Cockburn

Publication date: 12 October 2007

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

Full work available at URL: https://doi.org/10.1007/s10915-007-9129-9

zbMATH Keywords

numerical resultserror analysiserror boundsconvection-diffusion problemdiscontinuous Galerkin methodsuperconvergenceboundary value problemintegral functionalpostprocessingadjoint equations

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Error bounds for numerical methods for ordinary differential equations (65L70)

Related Items (3)

Adjoint-based, superconvergent Galerkin approximations of linear functionals ⋮ Post-processing discontinuous Galerkin solutions to Volterra integro-differential equations: analysis and simulations ⋮ Exploiting Superconvergence Through Smoothness-Increasing Accuracy-Conserving (SIAC) Filtering

Cites Work

• Galerkin approximations for the two point boundary problem using continuous, piecewise polynomial spaces
• Element-by-element post-processing of discontinuous Galerkin methods for Timoshenko beams
• Optimal a priori error estimates for the $hp$-version of the local discontinuous Galerkin method for convection--diffusion problems
• Superconvergence of the numerical traces of discontinuous Galerkin and Hybridized methods for convection-diffusion problems in one space dimension
• Discontinuous Galerkin Methods for Ordinary Differential Equations
• Higher Order Local Accuracy by Averaging in the Finite Element Method
• Adjoint Recovery of Superconvergent Functionals from PDE Approximations
• Enhanced accuracy by post-processing for finite element methods for hyperbolic equations
• Locking‐Free Optimal Discontinuous Galerkin Methods for Timoshenko Beams

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