arXiv

Finite elements for divdiv-conforming symmetric tensors

Long Chen and Xuehai Huang

arXiv:2005.01271

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ABSTRACT:

 Two types of finite element spaces on triangles are
constructed for div-div conforming symmetric tensors. Besides the
normal-normal continuity, the stress tensor is continuous at vertices
and another trace involving combination of derivatives of stress is
identified. Polynomial complex, finite element complex, and Hilbert
complex are presented and a commuting diagram between them is
given. The constructed div-div conforming elements are exploited to
discretize the mixed formulation of the biharmonic equation. Optimal
order and superconvergence error analysis is provided. By rotation,
finite elements for rot-rot conforming symmetric strain are also
obtained.