NORMAL-NORMAL CONTINUOUS SYMMETRIC STRESSES IN MIXED FINITE ELEMENT ELASTICITY

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dc.contributor.authorCarstensen, Carsten
dc.contributor.authorHeuer, Norbert
dc.date.accessioned2025-01-20T16:08:10Z
dc.date.available2025-01-20T16:08:10Z
dc.date.issued2024
dc.description.abstract. The classical continuous mixed formulation of linear elasticity with pointwise symmetric stresses allows for a conforming finite element discretization with piecewise polynomials of degree at least three. Symmetric stress approximations of lower polynomial order are only possible when their div-conformity is weakened to the continuity of normal-normal components. In two dimensions, this condition is meant pointwise along edges for piecewise polynomials, but a corresponding characterization for general piecewise H(div) tensors has been elusive. We introduce such a space and establish a continuous mixed formulation of linear planar elasticity with pointwise symmetric stresses that have, in a distributional sense, continuous normal-normal components across the edges of a shape-regular triangulation. The displacement is split into an L2 field and a tangential trace on the skeleton of the mesh. The well-posedness of the new mixed formulation follows with a duality lemma relating the normal-normal continuous stresses with the tangential traces of displacements. For this new formulation we present a lowest-order conforming discretization. Stresses are approximated by piecewise quadratic symmetric tensors, whereas displacements are discretized by piecewise linear polynomials. The tangential displacement trace acts as a Lagrange multiplier and guarantees global div-conformity in the limit as the mesh-size tends to zero. We prove locking-free, quasi-optimal convergence of our scheme and illustrate this with numerical examples.
dc.description.funderANID-Chile through FONDECYT
dc.fuente.origenWOS
dc.identifier.doi10.1090/mcom/4017
dc.identifier.eissn1088-6842
dc.identifier.issn0025-5718
dc.identifier.urihttps://doi.org/10.1090/mcom/4017
dc.identifier.urihttps://repositorio.uc.cl/handle/11534/90056
dc.identifier.wosidWOS:001319134000001
dc.language.isoen
dc.revistaMathematics of computation
dc.rightsacceso restringido
dc.titleNORMAL-NORMAL CONTINUOUS SYMMETRIC STRESSES IN MIXED FINITE ELEMENT ELASTICITY
dc.typeartículo
sipa.indexWOS
sipa.trazabilidadWOS;2025-01-12
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