A-posteriori error estimates for discontinuous Galerkin approximations of second order elliptic problems

DOI10.1007/s10915-009-9286-0zbMath1203.65257OpenAlexW2064132581MaRDI QIDQ618484

Luisa Donatella Marini, Carlo Lovadina

Publication date: 16 January 2011

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

Full work available at URL: https://doi.org/10.1007/s10915-009-9286-0

zbMATH Keywords

weighted residualsdiscontinuous finite elementsA-posteriori error estimates

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items

Pointwise error estimates and two-grid algorithms of discontinuous Galerkin method for strongly nonlinear elliptic problems ⋮ A Posteriori Error Estimates for a Modified Weak Galerkin Finite Element Approximation of Second Order Elliptic Problems with DG Norm ⋮ Foreword: Discontinuous Galerkin methods for partial differential equations ⋮ A posteriori error estimate for discontinuous Galerkin finite element method on polytopal mesh ⋮ Two-grid discontinuous Galerkin method for quasi-linear elliptic problems ⋮ A posteriori error estimates for HDG methods ⋮ A Fully Computable A Posteriori Error Estimate for the Stokes Equations on Polytopal Meshes ⋮ Goal-oriented error estimation based on equilibrated-flux reconstruction for finite element approximations of elliptic problems ⋮ Adaptive numerical solution of a discontinuous Galerkin method for a Helmholtz problem in low-frequency regime ⋮ Weak Galerkin based a posteriori error estimates for second order elliptic interface problems on polygonal meshes ⋮ A priori and a posterior error estimate of new weak Galerkin finite element methods for second order elliptic interface problems on polygonal meshes ⋮ A posteriori error estimator for exponentially fitted discontinuous Galerkin approximation of advection dominated problems

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• An a posteriori error estimate for the local discontinuous Galerkin method applied to linear and nonlinear diffusion problems
• Mixed discontinuous Galerkin methods for Darcy flow
• An a posteriori error estimate for the local discontinuous Galerkin method
• A high-order accurate discontinuous finite element method for the numerical solution of the compressible Navier-Stokes equations
• Compatible algorithms for coupled flow and transport
• On a mixed discontinuous Galerkin method
• Numerical validation of a class of mixed discontinuous Galerkin methods for Darcy flow
• A discontinuous \(hp\) finite element method for diffusion problems
• Energy norm a posteriori error estimation for discontinuous Galerkin methods.
• A posteriori error estimates for a discontinuous Galerkin method applied to elliptic problems
• A stabilized mixed finite element method for Darcy flow
• Discontinuous Galerkin methods. Theory, computation and applications. 1st international symposium on DGM, Newport, RI, USA, May 24--26, 1999
• Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. I
• Stabilization mechanisms in discontinuous Galerkin finite element methods
• A posteriori error estimates for mixed finite element approximations of elliptic problems
• An A Priori Error Analysis of the Local Discontinuous Galerkin Method for Elliptic Problems
• Quasi-Optimal Convergence Rate of an Adaptive Discontinuous Galerkin Method
• ENERGY NORM A POSTERIORI ERROR ESTIMATION OF hp-ADAPTIVE DISCONTINUOUS GALERKIN METHODS FOR ELLIPTIC PROBLEMS
• An Interior Penalty Finite Element Method with Discontinuous Elements
• Finite Element Methods for Elliptic Equations Using Nonconforming Elements
• An Elliptic Collocation-Finite Element Method with Interior Penalties
• The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
• A Posteriori Error Estimates for a Discontinuous Galerkin Approximation of Second-Order Elliptic Problems
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
• Local error analysis of the interior penalty discontinuous Galerkin method for second order elliptic problems
• Convergence Analysis of an Adaptive Interior Penalty Discontinuous Galerkin Method
• Convergence of Adaptive Discontinuous Galerkin Approximations of Second‐Order Elliptic Problems
• Symmetric and Nonsymmetric Discontinuous Galerkin Methods for Reactive Transport in Porous Media