An improved superconvergence error estimate for the LDG method

DOI10.1016/j.apnum.2015.07.005zbMath1329.65267OpenAlexW2251286055MaRDI QIDQ892711

Nabil Chaabane, Slimane Adjerid

Publication date: 11 November 2015

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

Full work available at URL: https://doi.org/10.1016/j.apnum.2015.07.005

zbMATH Keywords

finite element methodsuperconvergenceelliptic problemsdiscontinuous Galerkin

Mathematics Subject Classification ID

Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items (4)

Convergence and superconvergence of the local discontinuous Galerkin method for semilinear second-order elliptic problems on Cartesian grids ⋮ A Posteriori Error Estimates for a Local Discontinuous Galerkin Approximation of Semilinear Second-Order Elliptic Problems on Cartesian Grids ⋮ Optimal superconvergence and asymptotically exact \textit{a posteriori} error estimator for the local discontinuous Galerkin method for linear elliptic problems on Cartesian grids ⋮ Two efficient and reliable a posteriori error estimates for the local discontinuous Galerkin method applied to linear elliptic problems on Cartesian grids

Cites Work

• Foreword: Discontinuous Galerkin methods for partial differential equations
• A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations
• Asymptotically exact a posteriori error estimates for a one-dimensional linear hyperbolic problem
• The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems
• A superconvergent local discontinuous Galerkin method for elliptic problems
• An analysis of the minimal dissipation local discontinuous Galerkin method for convection-diffusion problems
• A posteriori local discontinuous Galerkin error estimation for two-dimensional convection-diffusion problems
• An A Priori Error Analysis of the Local Discontinuous Galerkin Method for Elliptic Problems
• Superconvergence of the Local Discontinuous Galerkin Method for Elliptic Problems on Cartesian Grids
• Optimal a priori error estimates for the $hp$-version of the local discontinuous Galerkin method for convection--diffusion problems
• TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• The Mathematical Theory of Finite Element Methods

This page was built for publication: An improved superconvergence error estimate for the LDG method