Optimal error estimates and superconvergence of an ultra weak discontinuous Galerkin method for fourth-order boundary-value problems

DOI10.1016/j.apnum.2018.11.011zbMath1434.65094OpenAlexW2902294258MaRDI QIDQ1728332

Mohamed Ben-Romdhane, Helmi Temimi, Mahboub Baccouch

Publication date: 22 February 2019

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

Full work available at URL: https://doi.org/10.1016/j.apnum.2018.11.011

zbMATH Keywords

Galerkin methoderror estimatessuperconvergenceboundary-value problemsupwind and downwind points

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Finite difference and finite volume methods for ordinary differential equations (65L12)

Related Items (3)

Superconvergent postprocessing of the \(C^1\)-conforming finite element method for fourth-order boundary value problems ⋮ Superconvergence Analysis of $C^m$ Finite Element Methods for Fourth-Order Elliptic Equations I: One Dimensional Case ⋮ 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

• Analysis of a posteriori error estimates of the discontinuous Galerkin method for nonlinear ordinary differential equations
• Superconvergence and a posteriori error estimates for the LDG method for convection-diffusion problems in one space dimension
• A posteriori error analysis of the discontinuous Galerkin method for two-dimensional linear hyperbolic conservation laws on Cartesian grids
• A local discontinuous Galerkin method for the second-order wave equation
• Asymptotically exact a posteriori LDG error estimates for one-dimensional transient convection-diffusion problems
• Superconvergence of the discontinuous Galerkin method for nonlinear second-order initial-value problems for ordinary differential equations
• 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
• A discontinuous Galerkin method for the wave equation
• Stability analysis and error estimates of local discontinuous Galerkin methods with implicit-explicit time-marching for nonlinear convection-diffusion problems
• A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations
• A discontinuous Galerkin method for higher-order ordinary differential equations
• An efficient method for fourth-order boundary value problems
• Asymptotically exact a posteriori error estimates for a one-dimensional linear hyperbolic problem
• Numerical solution of some ordinary differential equations occurring in plate deflection theory
• A discontinuous \(hp\) finite element method for convection-diffusion problems
• A posteriori error estimation for discontinuous Galerkin solutions of hyperbolic problems
• Superconvergence and \textit{a posteriori} error estimates of the DG method for scalar hyperbolic problems on Cartesian grids
• A Green element method for fourth order ordinary differential equations
• Parallel adaptive \(hp\)-refinement techniques for conservation laws
• A superconvergent local discontinuous Galerkin method for elliptic problems
• \textit{A posteriori} error estimates for a discontinuous Galerkin method applied to one-dimensional nonlinear scalar conservation laws
• The local discontinuous Galerkin method for linearized incompressible fluid flow: a review
• A posteriori error estimates and adaptivity for the discontinuous Galerkin solutions of nonlinear second-order initial-value problems
• The discontinuous Galerkin method for two-dimensional hyperbolic problems. I: Superconvergence error analysis
• Optimal a priori error estimates for the $hp$-version of the local discontinuous Galerkin method for convection--diffusion problems
• Superconvergence of Discontinuous Galerkin and Local Discontinuous Galerkin Schemes for Linear Hyperbolic and Convection-Diffusion Equations in One Space Dimension
• Superconvergence of the numerical traces of discontinuous Galerkin and Hybridized methods for convection-diffusion problems in one space dimension
• Superconvergence of Local Discontinuous Galerkin methods for one-dimensional linear parabolic equations
• Analysis of Sharp Superconvergence of Local Discontinuous Galerkin Method for One-Dimensional Linear Parabolic Equations
• TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
• An Interior Penalty Finite Element Method with Discontinuous Elements
• An Elliptic Collocation-Finite Element Method with Interior Penalties
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• Time Discretization of Parabolic Problems by the HP-Version of the Discontinuous Galerkin Finite Element Method
• Analysis of Optimal Superconvergence of Discontinuous Galerkin Method for Linear Hyperbolic Equations
• Optimal a Posteriori Error Estimates of the Local Discontinuous Galerkin Method for Convection-Diffusion Problems in One Space Dimension
• The Direct Discontinuous Galerkin (DDG) Methods for Diffusion Problems
• Adaptivity and Error Estimation for Discontinuous Galerkin Methods
• A discontinuous Galerkin finite element method for time dependent partial differential equations with higher order derivatives
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