A discourse on the stability conditions for mixed finite element formulations
Computer Methods in Applied Mechanics and Engineering
Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Stabilized Finite Element Formulations for Shells in a Bending Dominated State
SIAM Journal on Numerical Analysis
Measuring the convergence behavior of shell analysis schemes
Computers and Structures
A Lagrangian finite element approach for the simulation of water-waves induced by landslides
Computers and Structures
Improved stresses for the 4-node tetrahedral element
Computers and Structures
The MITC9 shell element in plate bending: mathematical analysis of a simplified case
Computational Mechanics
A stress improvement procedure
Computers and Structures
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When establishing and analyzing model-parameter dependent mixed formulations, it is common to consider required ellipticity and inf-sup conditions for the continuous and discrete problems. However, in the modeling of some important categories of problems, like in the analysis of plates and shells, the ellipticity condition usually considered does not naturally hold, and the inf-sup condition can only be stated in an abstract form and can hardly be evaluated analytically. In this paper we present a new and practical ellipticity condition which together with the inf-sup condition guarantees that (i) when the model parameter goes to zero, the limit problem solution is uniformly approached, and (ii) an optimal finite element discretization has been established (for the interpolations used). In practice, a numerical test might be performed to see whether the proposed ellipticity condition is satisfied.