Mixed finite elements for elasticity

By Douglas N. Arnold, Ragnar Winther. Numerische Mathematik, 2002

442 citations recorded by the source corpus.

Subfields: Biomedical Engineering, Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/63634b050f1c8d94c54d88a05add3e019608ad7f

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In Biomedical Engineering

In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

Convergence analysis of a new mixed finite element method for Biot's consolidation model (2014, methodology): “Recall that ∇ · Vh = Wh [20] and ∇ · h = Uh if d = ∅ [16].”
The Newmark scheme as velocity–stress time-staggering: an efficient PML implementation for spectral element simulations of elastodynamics (2005, methodology): “Even though promising direct consistent discretization of the stress space have been recently proposed (Arnold & Winther 2002; Bécache et al. 2002), high-order discretization preserving the geometrical flexibility of SE and the symmetry of the stress remains a challenging problem without resorting…”
Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book (2012, methodology): “The stability theory for mixed finite element discretizations originates from the work of Babuška (1973) and Brezzi (1974) in the early 1970’s.”
A Second Elasticity Element Using the Matrix Bubble (2012, background): “While it may be preferable to use finite elements that keep the exact symmetry of the stress tensor, the known symmetric stress elements for the mixed formulation have too many degrees of freedom to make it practically attractive [1, 3, 7].”
A review of unified a posteriori finite element error control (2012, unknown): “[7]).”
NONCONFORMING MIXED ELEMENTS FOR ELASTICITY (2003, background): “Mathematical Models and Methods in Applied Sciences Vol. 13, No. 3 (2003) 295–307 c© World Scientific Publishing Company”
Mixed finite element methods for incompressible flow: Stationary Stokes equations (2010, background): “The most significant ones are the increase in the number of unknowns and the symmetry requirement for the stress tensor [2].”
Finite element exterior calculus: From hodge theory to numerical stability (2009, methodology): “The plane elasticity elements of [11] were generalized to three dimensions in [3].”