A unified study of continuous and discontinuous Galerkin methods
From MaRDI portal
Publication:1729930
DOI10.1007/s11425-017-9341-1zbMath1412.65214arXiv1712.01211OpenAlexW2964178063WikidataQ128972668 ScholiaQ128972668MaRDI QIDQ1729930
Shuonan Wu, Fei Wang, Qingguo Hong, Jin-Chao Xu
Publication date: 7 March 2019
Published in: Science China. Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1712.01211
Error bounds for boundary value problems involving PDEs (65N15) 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) Second-order elliptic equations (35J15) Higher-order elliptic equations (35J30)
Related Items
Weak Galerkin Method for Second-Order Elliptic Equations with Newton Boundary Condition, Pressure robust hybrid mixed finite element method for Darcy–Forchheimer model, An extended Galerkin analysis in finite element exterior calculus, A mixed discontinuous Galerkin method for an unsteady incompressible Darcy equation, Developing stabilizer free weak Galerkin finite element method for second-order wave equation, A Posteriori Error Estimates for a Modified Weak Galerkin Finite Element Approximation of Second Order Elliptic Problems with DG Norm, A New Hybridized Mixed Weak Galerkin Method for Second-Order Elliptic Problems, A two-grid method for discontinuous Galerkin approximations to compressible miscible displacement problems, Discontinuous Galerkin methods for hemivariational inequalities in contact mechanics, Mean zero artificial diffusion for stable finite element approximation of convection in cellular aggregate formation, A mixed discontinuous Galerkin method for the wave equation, An extended Galerkin analysis for elliptic problems, A weak Galerkin-mixed finite element method for the Stokes-Darcy problem, An optimal piecewise cubic nonconforming finite element scheme for the planar biharmonic equation on general triangulations, A discontinuous Galerkin method for an elliptic hemivariational inequality for semipermeable media, A curl-conforming weak Galerkin method for the quad-curl problem, A mixed discontinuous Galerkin method with symmetric stress for Brinkman problem based on the velocity-pseudostress formulation, A priori error estimates of discontinuous Galerkin methods for a quasi-variational inequality, Adaptive discontinuous Galerkin methods for solving an incompressible Stokes flow problem with slip boundary condition of frictional type, Superconvergence of discontinuous Galerkin methods for elliptic boundary value problems, A mixed discontinuous Galerkin method for linear elasticity with strongly imposed symmetry, Weak Galerkin finite element method for viscoelastic wave equations, New discontinuous Galerkin algorithms and analysis for linear elasticity with symmetric stress tensor, A low-degree strictly conservative finite element method for incompressible flows on general triangulations, Robust approximation of generalized Biot-Brinkman problems, An over-penalized weak Galerkin method for parabolic interface problems with time-dependent coefficients
Cites Work
- Variational methods for the solution of problems of equilibrium and vibrations
- A weak Galerkin finite element method for the Stokes equations
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A posteriori error estimates for HDG methods
- \(C^0\) interior penalty methods for fourth order elliptic boundary value problems on polygonal domains
- Mixed discontinuous Galerkin methods for Darcy flow
- A new family of mixed finite elements in \({\mathbb{R}}^ 3\)
- A hybridizable discontinuous Galerkin method for fractional diffusion problems
- A hybridized discontinuous Galerkin method with reduced stabilization
- A weak Galerkin finite element method for the Maxwell equations
- A robust multigrid method for discontinuous Galerkin discretizations of Stokes and linear elasticity equations
- A three-dimensional quadratic nonconforming element
- Two families of mixed finite elements for second order elliptic problems
- Mixed finite elements for second order elliptic problems in three variables
- Mixed finite elements in \(\mathbb{R}^3\)
- Mixed-hybrid finite element approximations of second-order elliptic boundary-value problems
- A hybridizable discontinuous Galerkin formulation for non-linear elasticity
- Parameter-robust stability of classical three-field formulation of Biot's consolidation model
- A weak Galerkin finite element method for second-order elliptic problems
- On the local discontinuous Galerkin method for linear elasticity
- Approximation variationnelle des problèmes aux limites
- The Morley element for fourth order elliptic equations in any dimensions
- A variational principle and the convergence of a finite-element method based on assumed stress distribution
- On the finite element method
- Multipoint Taylor formulas and applications to the finite element method
- Approximation des problèmes aux limites non homogènes pour des opérateurs non linéaires
- A Hybridizable Discontinuous Galerkin Method for the $p$-Laplacian
- Contraction property of adaptive hybridizable discontinuous Galerkin methods
- Uniformly Stable Discontinuous Galerkin Discretization and Robust Iterative Solution Methods for the Brinkman Problem
- A Discontinuous Galerkin Method for the Fourth-Order Curl Problem
- Analysis of variable-degree HDG methods for Convection-Diffusion equations. Part II: Semimatching nonconforming meshes
- Basic principles of mixed Virtual Element Methods
- Conditions for superconvergence of HDG methods for second-order elliptic problems
- Superconvergent HDG Methods on Isoparametric Elements for Second-Order Elliptic Problems
- Analysis of an HDG method for linear elasticity
- Static Condensation, Hybridization, and the Devising of the HDG Methods
- Superconvergence by $M$-decompositions. Part I: General theory for HDG methods for diffusion
- Efficient rectangular mixed finite elements in two and three space variables
- A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems
- A weak Galerkin mixed finite element method for second order elliptic problems
- Hybridized globally divergence-free LDG methods. Part I: The Stokes problem
- Weak Galerkin Finite Element Methods on Polytopal Meshes
- Finite Element Interpolation of Nonsmooth Functions Satisfying Boundary Conditions
- Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems
- A Locally Conservative Finite Element Method Based on Piecewise Constant Enrichment of the Continuous Galerkin Method
- A projection-based error analysis of HDG methods
- New hybridization techniques
- A hybridizable discontinuous Galerkin method for linear elasticity
- A non-conforming piecewise quadratic finite element on triangles
- Mixed and nonconforming finite element methods : implementation, postprocessing and error estimates
- An Interior Penalty Finite Element Method with Discontinuous Elements
- Mixed and Hybrid Finite Element Methods
- Conforming and nonconforming finite element methods for solving the stationary Stokes equations I
- Alternate hybrid stress finite element models
- Primal Hybrid Finite Element Methods for 2nd Order Elliptic Equations
- An Elliptic Collocation-Finite Element Method with Interior Penalties
- The Local Discontinuous Galerkin Method for Time-Dependent Convection-Diffusion Systems
- Poincaré--Friedrichs Inequalities for Piecewise H1 Functions
- P1-Nonconforming Quadrilateral Finite Element Methods for Second-Order Elliptic Problems
- Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
- Devising superconvergent HDG methods with symmetric approximate stresses for linear elasticity by M-decompositions
- Quasi-Optimal Nonconforming Methods for Symmetric Elliptic Problems. I---Abstract Theory
- Interior penalty mixed finite element methods of any order in any dimension for linear elasticity with strongly symmetric stress tensor
- A primal-dual weak Galerkin finite element method for second order elliptic equations in non-divergence form
- Analysis of variable-degree HDG methods for convection-diffusion equations. Part I: general nonconforming meshes
- A Characterization of Hybridized Mixed Methods for Second Order Elliptic Problems
- Weak Galerkin method for the coupled Darcy–Stokes flow
- Quasi-Optimal Nonconforming Methods for Symmetric Elliptic Problems. III---Discontinuous Galerkin and Other Interior Penalty Methods
- Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems
- On a Class of Finite Elements Generated by Lagrange Interpolation
- BASIC PRINCIPLES OF VIRTUAL ELEMENT METHODS
- Minimal finite element spaces for $2m$-th-order partial differential equations in $R^n$
- Mixed Finite Element Methods and Applications
- A Posteriori Error Analysis for Hybridizable Discontinuous Galerkin Methods for Second Order Elliptic Problems
- Weak Galerkin finite element methods for elliptic PDEs
- Forty Years of the Crouzeix‐Raviart element
- The Direct Discontinuous Galerkin (DDG) Method for Diffusion with Interface Corrections
- The Direct Discontinuous Galerkin (DDG) Methods for Diffusion Problems
- Error analysis of variable degree mixed methods for elliptic problems via hybridization
- Incompressible Finite Elements via Hybridization. Part I: The Stokes System in Two Space Dimensions
- Incompressible Finite Elements via Hybridization. Part II: The Stokes System in Three Space Dimensions
- Convergence of the Mimetic Finite Difference Method for Diffusion Problems on Polyhedral Meshes
- The Staggered DG Method is the Limit of a Hybridizable DG Method
- Nonconforming Elements in the Finite Element Method with Penalty
- Basis of finite element methods for solid continua
- A FAMILY OF MIMETIC FINITE DIFFERENCE METHODS ON POLYGONAL AND POLYHEDRAL MESHES
- A generalization of the direct-stiffness method of structural analysis