A staggered DG method of minimal dimension for the Stokes equations on general meshes

DOI10.1016/j.cma.2018.11.016zbMath1440.76092OpenAlexW2902913767WikidataQ128871569 ScholiaQ128871569MaRDI QIDQ1986833

Dong-wook Shin, Eun-Jae Park, Li-Na Zhao

Publication date: 9 April 2020

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cma.2018.11.016

zbMATH Keywords

superconvergencepostprocessingstaggered gridlow regularityguaranteed upper boundequilibrated stress reconstructionlowest order SDG methodquadrilateral and polygonal meshes

Mathematics Subject Classification ID

Error bounds for boundary value problems involving PDEs (65N15) Stokes and related (Oseen, etc.) flows (76D07) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite element methods applied to problems in fluid mechanics (76M10)

Related Items (18)

A uniformly robust staggered DG method for the unsteady Darcy-Forchheimer-Brinkman problem ⋮ Novel adaptive hybrid discontinuous Galerkin algorithms for elliptic problems ⋮ A Strongly Mass Conservative Method for the Coupled Brinkman-Darcy Flow and Transport ⋮ A staggered cell-centered DG method for the biharmonic Steklov problem on polygonal meshes: a priori and a posteriori analysis ⋮ A staggered discontinuous Galerkin method for quasi-linear second order elliptic problems of nonmonotone type ⋮ A new staggered DG method for the Brinkman problem robust in the Darcy and Stokes limits ⋮ Error analysis for the pseudostress formulation of unsteady Stokes problem ⋮ An adaptive discontinuous Galerkin method for the Darcy system in fractured porous media ⋮ A parameter-free mixed formulation for the Stokes equations and linear elasticity with strongly symmetric stress ⋮ Staggered discontinuous Galerkin methods for the Helmholtz equation with large wave number ⋮ Staggered DG Methods for the Pseudostress-Velocity Formulation of the Stokes Equations on General Meshes ⋮ Staggered DG Method for Coupling of the Stokes and Darcy--Forchheimer Problems ⋮ A Staggered Cell-Centered DG Method for Linear Elasticity on Polygonal Meshes ⋮ Unnamed Item ⋮ A new hybrid staggered discontinuous Galerkin method on general meshes ⋮ Staggered DG method with small edges for Darcy flows in fractured porous media ⋮ Robust weak Galerkin finite element solvers for Stokes flow based on a lifting operator ⋮ A pressure robust staggered discontinuous Galerkin method for the Stokes equations

Cites Work

• Unnamed Item
• An arbitrary-order and compact-stencil discretization of diffusion on general meshes based on local reconstruction operators
• An adaptive SDG method for the Stokes system
• A mixed DG method for linearized incompressible magnetohydrodynamics
• A unified framework for a posteriori error estimation for the Stokes problem
• Mimetic finite difference method
• An optimal Poincaré inequality for convex domains
• A family of mixed finite elements for the elasticity problem
• A priori and a posteriori analysis of finite volume discretizations of Darcy's equations
• Guaranteed a posteriori error estimates for a staggered discontinuous Galerkin method
• A posteriori error estimates for the virtual element method
• Nonconforming finite volume methods
• Towards discrete Velte decompositions and narrow bounds for inf-sup constants
• Fully computable bounds for a staggered discontinuous Galerkin method for the Stokes equations
• Two Families of $H$(div) Mixed Finite Elements on Quadrilaterals of Minimal Dimension
• Optimal Discontinuous Galerkin Methods for the Acoustic Wave Equation in Higher Dimensions
• A Priori and A Posteriori Pseudostress-velocity Mixed Finite Element Error Analysis for the Stokes Problem
• A weak Galerkin mixed finite element method for second order elliptic problems
• Finite Element Methods for Navier-Stokes Equations
• A Posteriori Error Estimates for a Discontinuous Galerkin Approximation of Second-Order Elliptic Problems
• A Staggered Discontinuous Galerkin Method of Minimal Dimension on Quadrilateral and Polygonal Meshes
• Error Estimators for Nonconforming Finite Element Approximations of the Stokes Problem
• A Convergent Adaptive Algorithm for Poisson’s Equation
• BASIC PRINCIPLES OF VIRTUAL ELEMENT METHODS
• Reliable a posteriori error control for nonconforming finite element approximation of Stokes flow
• A Staggered Discontinuous Galerkin Method for the Stokes System
• Optimal Discontinuous Galerkin Methods for Wave Propagation
• The Mathematical Theory of Finite Element Methods
• The Staggered DG Method is the Limit of a Hybridizable DG Method
• QuadrilateralH(div) Finite Elements
• Postprocessing schemes for some mixed finite elements

This page was built for publication: A staggered DG method of minimal dimension for the Stokes equations on general meshes