A posteriori error estimate for discontinuous Galerkin finite element method on polytopal mesh

DOI10.1002/num.22443OpenAlexW2990608730MaRDI QIDQ6071663

Zhengjia Sun, Jintao Cui, Peng Zhu, Fuzheng Gao

Publication date: 28 November 2023

Published in: Numerical Methods for Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1002/num.22443

zbMATH Keywords

second-order elliptic problemsdiscontinuous Galerkin methodsa posteriori error estimatepolytopal mesh

Mathematics Subject Classification ID

Numerical analysis (65-XX) Partial differential equations (35-XX)

Cites Work

• Unnamed Item
• \texttt{PolyMesher}: a general-purpose mesh generator for polygonal elements written in Matlab
• A posteriori error estimates for HDG methods
• Virtual element methods for plate bending problems
• An a posteriori error estimate for the local discontinuous Galerkin method applied to linear and nonlinear diffusion problems
• Energy norm a posteriori error estimation for mixed discontinuous Galerkin approximations of the Stokes problem
• An a posteriori error estimate for the local discontinuous Galerkin method
• The discontinuous Galerkin method for two-dimensional hyperbolic problems. II: A posteriori error estimation
• A-posteriori error estimates for discontinuous Galerkin approximations of second order elliptic problems
• Mimetic finite difference method
• Extended finite element method on polygonal and quadtree meshes
• A framework for obtaining guaranteed error bounds for finite element approximations
• Energy norm a posteriori error estimation for discontinuous Galerkin methods.
• Fully computable a posteriori error bounds for hybridizable discontinuous Galerkin finite element approximations
• A hybrid high-order locking-free method for linear elasticity on general meshes
• A posteriori error estimates for the virtual element method
• 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.
• A polygonal finite element method for modeling arbitrary interfaces in large deformation problems
• Hybrid high-order methods for variable-diffusion problems on general meshes
• A virtual element method for elastic and inelastic problems on polytope meshes
• Contraction property of adaptive hybridizable discontinuous Galerkin methods
• Virtual Elements for Linear Elasticity Problems
• On the Adaptive Selection of the Parameter in Stabilized Finite Element Approximations
• $hp$-Version Composite Discontinuous Galerkin Methods for Elliptic Problems on Complicated Domains
• hp –Adaptive composite discontinuous Galerkin methods for elliptic problems on complicated domains
• Superconvergence byM-decompositions. Part II: Construction of two-dimensional finite elements
• Superconvergence byM-decompositions. Part III: Construction of three-dimensional finite elements
• Superconvergence by $M$-decompositions. Part I: General theory for HDG methods for diffusion
• Quasi-Optimal Convergence Rate of an Adaptive Discontinuous Galerkin Method
• Discontinuous Galerkin Finite Element Methods for Interface Problems: A Priori and A Posteriori Error Estimations
• A weak Galerkin mixed finite element method for second order elliptic problems
• Some Estimates for a Weighted L 2 Projection
• ENERGY NORM A POSTERIORI ERROR ESTIMATION OF hp-ADAPTIVE DISCONTINUOUS GALERKIN METHODS FOR ELLIPTIC PROBLEMS
• A Posteriori Error Estimation for Discontinuous Galerkin Finite Element Approximation
• Theory of adaptive finite element methods: An introduction
• A‐posteriori error estimates for the finite element method
• Edge Residuals Dominate A Posteriori Error Estimates for Low Order Finite Element Methods
• A Posteriori Error Estimates for a Discontinuous Galerkin Approximation of Second-Order Elliptic Problems
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
• A Convergent Adaptive Algorithm for Poisson’s Equation
• BASIC PRINCIPLES OF VIRTUAL ELEMENT METHODS
• A Posteriori Error Analysis for Hybridizable Discontinuous Galerkin Methods for Second Order Elliptic Problems
• Post processing of solution and flux for the nodal mimetic finite difference method
• Residuala posteriorierror estimation for the Virtual Element Method for elliptic problems
• Convergence Analysis of an Adaptive Interior Penalty Discontinuous Galerkin Method
• Convergence of Adaptive Discontinuous Galerkin Approximations of Second‐Order Elliptic Problems
• Convergence of the Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes
• hp-Version discontinuous Galerkin methods on polygonal and polyhedral meshes
• Conforming polygonal finite elements

This page was built for publication: A posteriori error estimate for discontinuous Galerkin finite element method on polytopal mesh