A symmetric mixed finite element method for nearly incompressible elasticity based on biorthogonal systems

DOI10.1002/num.20683zbMath1345.74102OpenAlexW2168982157WikidataQ59889882 ScholiaQ59889882MaRDI QIDQ2910813

Bishnu P. Lamichhane, Ernst Peter Stephan

Publication date: 11 September 2012

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

Full work available at URL: https://doi.org/10.1002/num.20683

zbMATH Keywords

mixed finite elementssymmetric systemGalerkin discretizationbiorthogonal systemPetrov

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Finite element methods applied to problems in solid mechanics (74S05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items (9)

A LOCAL PROJECTION STABILIZATION FOR CONVECTION–DIFFUSION–REACTION EQUATIONS USING BIORTHOGONAL SYSTEMS ⋮ A mixed finite element method for the Poisson problem using a biorthogonal system with <scp>Raviart–Thomas</scp> elements ⋮ Mixed finite element methods for the Poisson equation using biorthogonal and quasi-biorthogonal systems ⋮ A locking-free solver for linear elasticity on quadrilateral and hexahedral meshes based on enrichment of Lagrangian elements ⋮ Lowest-order weak Galerkin finite element methods for linear elasticity on rectangular and brick meshes ⋮ Mixed Kirchhoff stress-displacement-pressure formulations for incompressible hyperelasticity ⋮ Integrated heart -- coupling multiscale and multiphysics models for the simulation of the cardiac function ⋮ An extension of the Crouzeix–Raviart space to general meshes with application to quasi-incompressible linear elasticity and Stokes flow ⋮ A new stabilization technique for the nonconforming Crouzeix-Raviart element applied to linear elasticity

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A stable finite element for the Stokes equations
• Uniform convergence and a posteriori error estimators for the enhanced strain finite element method
• An a priori error estimate for finite element discretizations in nonlinear elasticity for polyconvex materials under small loads
• Convergence in the incompressible limit of finite element approximations based on the Hu-Washizu formulation
• Higher order mortar finite element methods in 3D with dual Lagrange multiplier bases
• Well‐posedness and numerical performances of the strain gap method
• On the formulation of enhanced strain finite elements in finite deformations
• A mixed finite element method for non-linear and nearly incompressible elasticity based on biorthogonal systems
• Finite Element Methods for Navier-Stokes Equations
• Generalized Inf-Sup Conditions for Chebyshev Spectral Approximation of the Stokes Problem
• Existence, Uniqueness and Approximation for Generalized Saddle Point Problems
• Mixed and Hybrid Finite Element Methods
• Geometrically non-linear enhanced strain mixed methods and the method of incompatible modes
• Linear Finite Element Methods for Planar Linear Elasticity
• A Mortar Finite Element Method Using Dual Spaces for the Lagrange Multiplier
• Stability of saddle point problems with penalty
• Stability and Convergence of a Class of Enhanced Strain Methods
• A class of mixed assumed strain methods and the method of incompatible modes

This page was built for publication: A symmetric mixed finite element method for nearly incompressible elasticity based on biorthogonal systems