The local discontinuous Galerkin method for the fourth-order Euler-Bernoulli partial differential equation in one space dimension. II: A posteriori error estimation

DOI10.1007/s10915-013-9783-zzbMath1462.65137OpenAlexW2003236687WikidataQ115382695 ScholiaQ115382695MaRDI QIDQ474920

Mahboub Baccouch

Publication date: 25 November 2014

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

Full work available at URL: https://doi.org/10.1007/s10915-013-9783-z

zbMATH Keywords

superconvergencea posteriori error estimateslocal discontinuous Galerkin methodRadau pointsadaptive mesh methodfourth-order Euler-Bernoulli equation

Mathematics Subject Classification ID

Finite element methods applied to problems in solid mechanics (74S05) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50) PDEs in connection with mechanics of deformable solids (35Q74)

Related Items (21)

Asymptotically exact a posteriori local discontinuous Galerkin error estimates for the one-dimensional second-order wave equation ⋮ Superconvergence and \textit{a posteriori} error estimates of the DG method for scalar hyperbolic problems on Cartesian grids ⋮ A posteriori error estimates and adaptivity for the discontinuous Galerkin solutions of nonlinear second-order initial-value problems ⋮ Analysis of optimal superconvergence of the local discontinuous Galerkin method for nonlinear fourth-order boundary value problems ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ Unnamed Item ⋮ An adaptive local discontinuous Galerkin method for nonlinear two-point boundary-value problems ⋮ Efficient high-order physical property-preserving difference methods for nonlinear fourth-order wave equation with damping ⋮ A superconvergent ultra-weak local discontinuous Galerkin method for nonlinear fourth-order boundary-value problems ⋮ Analysis of the lumped mass model for the cantilever beam subject to Grob's swelling pressure ⋮ The local discontinuous Galerkin method for the fourth-order Euler-Bernoulli partial differential equation in one space dimension. I: Superconvergence error analysis ⋮ A discontinuous Galerkin method and its error estimate for nonlinear fourth-order wave equations ⋮ Superconvergence of discontinuous Galerkin solutions for higher-order ordinary differential equations ⋮ Two conservative and linearly-implicit compact difference schemes for the nonlinear fourth-order wave equation ⋮ A posteriori local discontinuous Galerkin error estimation for two-dimensional convection-diffusion problems ⋮ A Superconvergent Local Discontinuous Galerkin Method for Nonlinear Fourth-Order Boundary-Value Problems ⋮ Study of the backward difference and local discontinuous Galerkin (LDG) methods for solving fourth-order partial integro-differential equations (PIDEs) with memory terms: stability analysis

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• A local discontinuous Galerkin method for the second-order wave equation
• The local discontinuous Galerkin method for the fourth-order Euler-Bernoulli partial differential equation in one space dimension. I: Superconvergence error analysis
• Asymptotically exact a posteriori LDG error estimates for one-dimensional transient convection-diffusion problems
• Superconvergence of discontinuous finite element solutions for transient convection-diffusion problems
• The discontinuous Galerkin method for two-dimensional hyperbolic problems. II: A posteriori error estimation
• Discontinuous Galerkin error estimation for hyperbolic problems on unstructured triangular meshes
• Asymptotically exact a posteriori error estimates for a one-dimensional linear hyperbolic problem
• A posteriori error estimation for discontinuous Galerkin solutions of hyperbolic problems
• A posteriori error estimates for a discontinuous Galerkin method applied to elliptic problems
• A posteriori discontinuous finite element error estimation for two-dimensional hyperbolic problems.
• Error estimation for discontinuous Galerkin solutions of two-dimensional hyperbolic problems
• Discontinuous Galerkin methods. Theory, computation and applications. 1st international symposium on DGM, Newport, RI, USA, May 24--26, 1999
• \textit{A posteriori} error estimates for a discontinuous Galerkin method applied to one-dimensional nonlinear scalar conservation laws
• Superconvergence of discontinuous Galerkin solutions for a nonlinear scalar hyperbolic problem
• The discontinuous Galerkin method for two-dimensional hyperbolic problems. I: Superconvergence error analysis
• Superconvergence of Discontinuous Galerkin and Local Discontinuous Galerkin Schemes for Linear Hyperbolic and Convection-Diffusion Equations in One Space Dimension
• ENERGY NORM A POSTERIORI ERROR ESTIMATION OF hp-ADAPTIVE DISCONTINUOUS GALERKIN METHODS FOR ELLIPTIC PROBLEMS
• Asymptotically exact a posteriori local discontinuous Galerkin error estimates for the one-dimensional second-order wave equation
• Adaptive Discontinuous Galerkin Finite Element Methods for Nonlinear Hyperbolic Conservation Laws
• Error Estimates for Finite Element Methods for Scalar Conservation Laws
• Analysis of Optimal Superconvergence of Discontinuous Galerkin Method for Linear Hyperbolic Equations
• Adaptivity and Error Estimation for Discontinuous Galerkin Methods

This page was built for publication: The local discontinuous Galerkin method for the fourth-order Euler-Bernoulli partial differential equation in one space dimension. II: A posteriori error estimation