To \(\mathcal{P}\) or not to \(p\) -- the mixed displacement-pressure \(p\), versus the higher order \(\mathcal{P}\) displacement finite element formulation, for nearly incompressible linear elasticity

Navier-Stokes equations for incompressible viscous fluids (76D05) 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) Finite element methods applied to problems in fluid mechanics (76M10)

Cites Work

On the role of the Helmholtz decomposition in mixed methods for incompressible flows and a new variational crime
Locking effects in the finite element approximation of elasticity problems
Analytical and computational assessment of locking in the \(hp\) finite element method
A remark on finite element schemes for nearly incompressible elasticity
Legendre spectral element method with nearly incompressible materials
Mixed \(hp\) finite element methods for problems in elasticity and Stokes flow
Locking-free and gradient-robust \(H(\operatorname{div})\)-conforming HDG methods for linear elasticity
High order exactly divergence-free Hybrid Discontinuous Galerkin methods for unsteady incompressible flows
Pressure-robustness and discrete Helmholtz projectors in mixed finite element methods for the incompressible Navier-Stokes equations
A variational principle for incompressible and nearly-incompressible anisotropic elasticity
The finite element method with Lagrangian multipliers
Locally conservative discontinuous Petrov-Galerkin finite elements for fluid problems
On pressure robustness and independent determination of displacement and pressure in incompressible linear elasticity
Robust Arbitrary Order Mixed Finite Element Methods for the Incompressible Stokes Equations with pressure independent velocity errors
Finite Element Methods for Incompressible Flow Problems
Norm estimates for a maximal right inverse of the divergence operator in spaces of piecewise polynomials
Perturbation of mixed variational problems. Application to mixed finite element methods
On Locking and Robustness in the Finite Element Method
Computing with hp-ADAPTIVE FINITE ELEMENTS
Divergence-free Reconstruction Operators for Pressure-Robust Stokes Discretizations with Continuous Pressure Finite Elements
On the Divergence Constraint in Mixed Finite Element Methods for Incompressible Flows
Stress computations for nearly incompressible materials by the p‐version of the finite element method
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