Rigorous stability and interpolation estimates for Hellinger-Reissner virtual elements with constants depending only on mesh aspect ratio and polynomial degree, plus numerical evidence that degenerate shapes degrade the constants.
The Johnson-Krizek-Mercier elasticity element in any dimensions
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abstract
Mixed methods for linear elasticity with strongly symmetric stresses of lowest order are studied in this paper. On each simplex, the stress space has piecewise linear components with respect to its Alfeld split (which connects the vertices to barycenter), generalizing the Johnson--Mercier two-dimensional element to higher dimensions. Further reductions in the stress space in the three-dimensional case (to 24 degrees of freedom per tetrahedron) are possible when the displacement space is reduced to local rigid displacements. Proofs of optimal error estimates of numerical solutions and improved error estimates via postprocessing and the duality argument are presented.
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Stability and interpolation estimates of Hellinger-Reissner virtual element spaces
Rigorous stability and interpolation estimates for Hellinger-Reissner virtual elements with constants depending only on mesh aspect ratio and polynomial degree, plus numerical evidence that degenerate shapes degrade the constants.