Inf–sup conditions for twofold saddle point problems

No abstract is available for this paper.

• Publication year

  2011

• Venue

  Numerische Mathematik

• Publication date

  2011-08-01

• Fields of study

  Mathematics, Computer Science, Engineering

• Identifiers
  DOI 10.1007/s00211-011-0372-5
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

• Mixed and Hybrid Finite Element Methods

  2011influential reference
• Analysis of Mixed Finite Element Methods for the Stokes Problem: A Unified Approach

  2010cited by this paper
• A POSTERIORI ERROR ESTIMATION FOR A DUAL MIXED FINITE ELEMENT APPROXIMATION OF NON{NEWTONIAN FLUID FLOW PROBLEMS

  2008cited by this paper
• A new dual-mixed finite element method for the plane linear elasticity problem with pure traction boundary conditions☆

  2008cited by this paper
• A dual-mixed approximation method for a three-field model of a nonlinear generalized Stokes problem

  2008cited by this paper
• Characterizing the inf-sup condition on product spaces

  2008cited by this paper
• Finite elements for symmetric tensors in three dimensions

  2007influential reference
• Mixed finite element methods for linear elasticity with weakly imposed symmetry

  2007cited by this paper
• Coupled Generalized Nonlinear Stokes Flow with flow through a Porous Media

  2007influential reference
• A dual-mixed finite element method for nonlinear incompressible elasticity with mixed boundary conditions

  2007cited by this paper
• Differential complexes and stability of finite element methods. I. The de Rham complex

  2006cited by this paper
• Defferential Complexes and Stability of Finite Element Methods II: The Elasticity Complex

  2006cited by this paper
• On the a priori and a posteriori error analysis of a two‐fold saddle‐point approach for nonlinear incompressible elasticity

  2006cited by this paper
• Enriched finite element subspaces for dual-dual mixed formulations in fluid mechanics and elasticity

  2005cited by this paper
• Error analysis of variable degree mixed methods for elliptic problems via hybridization

  2005cited by this paper
• A low-order mixed finite element method for a class of quasi-Newtonian Stokes flows. Part I: a priori error analysis

  2004cited by this paper
• On the numerical analysis of nonlinear twofold saddle point problems

  2003cited by this paper
• Solvability and Galerkin Approximations of a Class of Nonlinear Operator Equations

  2002cited by this paper
• Mixed finite elements for elasticity

  2002influential reference
• A mixed‐FEM formulation for nonlinear incompressible elasticity in the plane

  2002cited by this paper
• A FULLY DISCRETE GALERKIN SCHEME FOR A TWO-FOLD SADDLE POINT FORMULATION OF AN EXTERIOR NONLINEAR PROBLEM *

  2001cited by this paper
• Mixed finite element analysis of a non‐linear three‐fields Stokes model

  2001cited by this paper
• Dual combined finite element methods for Non-Newtonian flow (II) parameter-dependent problem

  2000cited by this paper
• Expanded mixed finite element methods for linear second-order elliptic problems, I

  1998cited by this paper
• Dual hybrid methods for the elasticity and the Stokes problems: a unified approach

  1997cited by this paper
• Analysis of expanded mixed methods for fourth‐order elliptic problems

  1997influential reference
• The Mathematical Theory of Finite Element Methods

  1994cited by this paper
• Quasi-norm error bounds for the finite element approximation of a non-Newtonian flow

  1994cited by this paper
• Numerical analysis of a three-fields model for a quasi-Newtonian flow

  1993cited by this paper
• Finite element error analysis of a quasi-Newtonian flow obeying the Carreau or power law

  1993cited by this paper
• A new mixed finite element for the Stokes and elasticity problems

  1993cited by this paper
• Mixed and hybrid methods

  1991cited by this paper
• Mixed and hybrid finite element methods

  1987cited by this paper
• Finite Element Methods for Navier-Stokes Equations - Theory and Algorithms

  1986cited by this paper
• A family of higher order mixed finite element methods for plane elasticity

  1984cited by this paper
• PEERS: A new mixed finite element for plane elasticity

  1984influential reference
• A mixed finite element method for the Navier-Stokes equations

  1978cited by this paper
• Existence et approximation de points selles pour certains problèmes non linéaires

  1977cited by this paper
• Sur l'approximation, par éléments finis d'ordre un, et la résolution, par pénalisation-dualité d'une classe de problèmes de Dirichlet non linéaires

  1975cited by this paper
• On the existence, uniqueness and approximation of saddle-point problems arising from lagrangian multipliers

  1974cited by this paper
• The finite element method with Lagrangian multipliers

  1973cited by this paper

• Scalable augmented Lagrangian preconditioners for fictitious domain problems

  2025influential citation
• Preconditioning a hybridizable discontinuous Galerkin method for Navier-Stokes at high Reynolds number

  2025influential citation
• On parameter identification in the Stokes system with threshold leak boundary conditions

  2025influential citation
• Optimal Control of a Hemivariational Inequality of Stationary Convective Brinkman-Forchheimer Extended Darcy equations with Numerical Approximation

  2025influential citation
• Mixed Finite Element Method for a Hemivariational Inequality of Stationary convective Brinkman-Forchheimer Extended Darcy equations

  2025influential citation
• Mixed Virtual Element Approximation for the Five-Field Formulation of the Steady Boussinesq Problem with Temperature-Dependent Parameters

  2024influential citation
• On the improvement of shift-splitting preconditioners for double saddle point problems

  2024cites this paper
• A strongly conservative hybridizable discontinuous Galerkin method for the coupled time-dependent Navier-Stokes and Darcy problem

  2023influential citation
• A hybridizable discontinuous Galerkin method for the dual-porosity-Stokes problem

  2023cites this paper
• Design and analysis of a hybridized discontinuous Galerkin method for incompressible flows on meshes with quadrilateral cells

  2023cites this paper
• New twofold saddle-point formulations for Biot poroelasticity with porosity-dependent permeability

  2023cites this paper
• Trefftz discontinuous Galerkin discretization for the Stokes problem

  2023cites this paper
• Design and analysis of an exactly divergence-free hybridised discontinuous Galerkin method for incompressible flows on meshes with quadrilateral cells

  2023influential citation
• Robust finite element discretizations for a simplified Galbrun's equation

  2022cites this paper
• FETI-DP algorithms for 2D Biot model with discontinuous Galerkin discretization

  2022cites this paper
• FETI-DP preconditioners for 2D Biot model with discontinuous Galerkin discretization

  2022cites this paper
• A hybridizable discontinuous Galerkin method for the coupled Navier-Stokes and Darcy problem

  2022cites this paper
• Analysis of an Embedded-Hybridizable Discontinuous Galerkin Method for Biot’s Consolidation Model

  2022influential citation
• Hybridizable discontinuous Galerkin methods for the coupled Stokes-Biot problem

  2022influential citation
• Space-time reduced basis methods for parametrized unsteady Stokes equations

  2022influential citation
• An Algebraic Preconditioner for the Exactly Divergence‐Free Discontinuous Galerkin Method for Stokes

  2022influential citation
• An offline multi‐scale unsaturated poromechanics model enabled by self‐designed/self‐improved neural networks

  2021cites this paper
• Robust Approximation of Generalized Biot-Brinkman Problems

  2021influential citation
• A review on phase-field modeling of hydraulic fracturing

  2021cites this paper
• Analysis of a momentum conservative mixed‐FEM for the stationary Navier–Stokes problem

  2021cites this paper
• Schur complement based preconditioners for twofold and block tridiagonal saddle point problems

  2021cites this paper
• Variational formulation of marine ice-sheet and subglacial-lake grounding-line dynamics

  2021influential citation
• A divergence-free finite element method for the Stokes problem with boundary correction

  2021cites this paper
• Preconditioning for a pressure-robust HDG discretization of the Stokes equations

  2021cites this paper
• Existence of a weak solution to a steady 2D fluid-1D elastic structure interaction problem with Tresca slip boundary condition

  2021cites this paper
• Analysis of an exactly mass conserving space-time hybridized discontinuous Galerkin method for the time-dependent Navier-Stokes equations

  2021cites this paper
• A pressure-robust embedded discontinuous Galerkin method for the Stokes problem by reconstruction operators

  2020cites this paper
• A Banach spaces-based analysis of a new fully-mixed finite element method for the Boussinesq problem

  2020cites this paper
• A phase field framework for capillary-induced fracture in unsaturated porous media: Drying-induced vs. hydraulic cracking

  2020cites this paper
• Two-level Galerkin Mixed Finite Element Method for Darcy-Forchheimer Model in Porous Media

  2020cites this paper
• Rotation-Based Mixed Formulations for an Elasticity-Poroelasticity Interface Problem

  2020cites this paper
• Upscaling LBM-TPM simulation approach of Darcy and non-Darcy fluid flow in deformable, heterogeneous porous media

  2020cites this paper
• A fully-mixed finite element method for the steady state Oberbeck–Boussinesq system

  2020cites this paper
• An accelerated hybrid data-driven/model-based approach for poroelasticity problems with multi-fidelity multi-physics data

  2020cites this paper
• Stokes Problem with Slip Boundary Conditions of Friction Type: Error Analysis of a Four-Field Mixed Variational Formulation

  2019cites this paper
• A generalized inf–sup test for multi-field mixed-variational methods

  2019cites this paper
• Stokes system with local Coulomb's slip boundary conditions: Analysis of discretized models and implementation

  2019cites this paper
• Stabilized mixed continuous/enriched Galerkin formulations for locally mass conservative poromechanics

  2019cites this paper
• Preconditioning of a Hybridized Discontinuous Galerkin Finite Element Method for the Stokes Equations

  2018influential citation
• An embedded-hybridized discontinuous Galerkin finite element method for the Stokes equations

  2018cites this paper
• Strain localization in a solid‐water‐air system with random heterogeneity via stabilized mixed finite elements

  2017cites this paper
• Computational thermo-hydro-mechanics for multiphase freezing and thawing porous media in the finite deformation range

  2017cites this paper
• Mixed Arlequin method for multiscale poromechanics problems

  2017cites this paper
• Hydromechanical Modeling of Unsaturated Flow in Double Porosity Media

  2016cites this paper
• Final Report: A multiscale analysis on the moisture effect of dynamics responses of granular matters

  2016cites this paper
• Numerical Approximations of Problems That Arise in Elasticity

  2016cites this paper
• An Augmented Mixed Finite Element Method for the Navier-Stokes Equations with Variable Viscosity

  2016cites this paper
• A Dual–Mixed Finite Element Method for the Brinkman Problem

  2016cites this paper
• Dual-Mixed Finite Element Methods for the Navier-Stokes Equations

  2016cites this paper
• Prestructuring sparse matrices with dense rows and columns via null space methods

  2015cites this paper
• A stabilized finite element formulation for monolithic thermo‐hydro‐mechanical simulations at finite strain

  2015influential citation
• Primal-mixed formulations for reaction-diffusion systems on deforming domains

  2015cites this paper
• Fluid Model of Crystal Plasticity

  2015cites this paper
• Finite element approximation of Stokes-like systems with implicit constitutive relation

  2015cites this paper
• Stabilized mixed finite elements for deformable porous media with double porosity

  2015influential citation
• Stokes problem with a solution dependent slip bound: Stability of solutions with respect to domains

  2015influential citation
• Babuška–Brezzi Theory

  2014cites this paper
• Mixed Finite Element Methods

  2014cites this paper
• Numerical analysis of the flows in the pebble bed geometries

  2014cites this paper
• Locking-free compressible quadrilateral finite elements: Poisson’s ratio-dependent vector interpolants

  2014cites this paper
• Numerical experiments of dynamical processes during the 2011-2013 surge of the Bering-Bagley Glacier System, using a full-Stokes finite element model

  2014cites this paper
• Raviart-Thomas Spaces

  2014cites this paper
• A New Family of Efficient Conforming Mixed Finite Elements on Both Rectangular and Cuboid Meshes for Linear Elasticity in the Symmetric Formulation

  2013cites this paper
• Characterization of the Solvability of Generalized Constrained Variational Equations

  2012cites this paper
• Research Statement 1 Numerical Analysis and Computation of Fluid / Fluid and Fluid / Structure Interaction Problems

  2011cites this paper
• Approximation of generalized Stokes problems using dual‐mixed finite elements without enrichment

  2011cites this paper
• Analysis and Finite Element Approximation of a Nonlinear Stationary Stokes Problem Arising in Glaciology

  2011cites this paper
• Modélisation, analyse mathématique et simulation numérique de la dynamique des glaciers

  2010cites this paper
• Approximation of generalized and steady Stokes problems using dual-mixed finite elements without enrichment

  2009cites this paper