The inf–sup condition and its evaluation for mixed finite element methods

By Klaus-Jürgen Bathe. 2001

319 citations recorded by the source corpus.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/af86d883e608afadc19f0282fc1d68d89233810b

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In Computational Mechanics

In Electrical and Electronic Engineering

In Mechanics of Materials

Citations in the corpus

A modified node‐to‐segment algorithm passing the contact patch test (2009, methodology): “Finally, there is no proof that the proposed formulation satisfies the inf–sup (or LBB) condition, which characterizes the numerical stability of mixed method approaches [24].”
The MITC3 shell finite element enriched by interpolation covers (2014, background): “The s-norm is suitable to check whether the finite element solutions satisfy consistency and the inf-sup condition [36–40], and is defined as follows ku uhks 1⁄4 Z”
Non-commercial Research and Educational Use including without Limitation Use in Instruction at Your Institution, Sending It to Specific Colleagues That You Know, and Providing a Copy to Your Institution's Administrator. All Other Uses, Reproduction and Distribution, including without Limitation Comm (2005, unknown): “In our GA-fit, a two-step procedure was implemented.”
A stable 3D contact formulation using X-FEM (2007, background): “To assure that, the ellipticity and the inf-sup (or LBB) conditions must be satisfied (Bathe, 2001).”
Stability of incompressible formulations enriched with X-FEM (2008, background): “This test proved to be useful for the study of the stability of various mixed elements [12].”
A meshfree method: meshfree weak–strong (MWS) form method, for 2-D solids (2003, background): “De and Bathe (De and Bathe 2001) found this problem and studied it in very detail ( Bathe 2001; De and Bathe 2001).”
Displacement/pressure mixed interpolation in the method of finite spheres (2001, methodology): “The inf–sup condition To obtain a stable and optimal procedure for the selected interpolations, the mixed formulation in Equations (21) and (22) should satisfy the ellipticity condition (readily satis ed in this linear analysis since no reduced integration is used) and the inf–sup condition [2; 3]”
A finite element method enriched for wave propagation problems (2012, methodology): “While we have presented the method for the displacementbased method of finite elements – with all the important properties directly applicable [2] – it would be valuable to extend the method for the u/p formulation (for incompressible analysis) and the MITC formulations for beams, plates and shells ”
The MITC3+shell element and its performance (2014, unknown): “The s-norm is suitable to identify whether the finite element formulation satisfies the consistency and inf–sup conditions [3,31–33].”
Supremizer stabilization of POD–Galerkin approximation of parametrized steady incompressible Navier–Stokes equations (2015, background): “Further details about possible ways to express (and check) the inf-sup condition can be found, for example, in [42, 43, 47, 48].”
Finite element developments for general fluid flows with structural interactions (2004, methodology): “These are the same pairs of functions that are, for example, also used in the analysis of solids or acoustic fluids [9, 22, 23].”
Discretizations in isogeometric analysis of Navier-Stokes flow (2011, unknown): “To test the stability of the discretization strategies, we use the approach described in [18, 19].”