An observation on Korn’s inequality for nonconforming finite element methods

DOI10.1090/S0025-5718-05-01783-7zbMath1086.65112OpenAlexW1983001190MaRDI QIDQ5713215

Kent-André Mardal, Ragnar Winther

Publication date: 12 December 2005

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-05-01783-7

zbMATH Keywords

error boundnonconforming finite elementsKorn's inequalitypiecewise \(H^1\) vector fields

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Finite element methods applied to problems in solid mechanics (74S05) 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 (16)

Anisotropic mixed finite elements for elasticity ⋮ A nonconforming finite element method for the Biot's consolidation model in poroelasticity ⋮ Robust three-field finite element methods for Biot's consolidation model in poroelasticity ⋮ A discrete de Rham complex with enhanced smoothness ⋮ A convergent FEM-DG method for the compressible Navier-Stokes equations ⋮ Two robust nonconforming \(H^2\)-elements for linear strain gradient elasticity ⋮ A divergence free weak virtual element method for the Stokes problem on polytopal meshes ⋮ Transformations for Piola-mapped elements ⋮ Divergence-conforming velocity and vorticity approximations for incompressible fluids obtained with minimal facet coupling ⋮ A virtual element method for overcoming locking phenomena in Biot’s consolidation model ⋮ Nonconforming finite element approximation of the Giesekus model for polymer flows ⋮ \(H\)(div) conforming finite element methods for the coupled Stokes and Darcy problem ⋮ Piecewise $\mathbf {H^1}$ functions and vector fields associated with meshes generated by independent refinements ⋮ Unified finite element discretizations of coupled Darcy-Stokes flow ⋮ \(H^2\)-Korn's inequality and the nonconforming elements for the strain gradient elastic model ⋮ A Nitsche cut finite element method for the Oseen problem with general Navier boundary conditions

Cites Work

• Nonconforming Finite Element Methods for the Equations of Linear Elasticity
• Conforming and nonconforming finite element methods for solving the stationary Stokes equations I
• A Robust Finite Element Method for Darcy--Stokes Flow
• Korn's inequalities for piecewise $H^1$ vector fields

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