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FINITE ELEMENTS FOR SYMMETRIC TENSORS IN THREE DOUGLAS N. ARNOLD, GERARD AWANOU, AND RAGNAR WINTHER
 

Summary: PREPRINT
FINITE ELEMENTS FOR SYMMETRIC TENSORS IN THREE
DIMENSIONS
DOUGLAS N. ARNOLD, GERARD AWANOU, AND RAGNAR WINTHER
Abstract. We construct finite element subspaces of the space of symme-
tric tensors with square-integrable divergence on a three-dimensional domain.
These spaces can be used to approximate the stress field in the classical
Hellinger­Reissner mixed formulation of the elasticty equations, when stan-
dard discontinuous finite element spaces are used to approximate the displace-
ment field. These finite element spaces are defined with respect to an arbitrary
simplicial triangulation of the domain, and there is one for each positive value
of the polynomial degree used for the displacements. For each degree, these
provide a stable finite element discretization. The construction of the spaces
is closely tied to discretizations of the elasticity complex, and can be viewed
as the three-dimensional analogue of the triangular element family for plane
elasticity previously proposed by Arnold and Winther.
1. Introduction
The classical Lagrange finite element spaces provide natural simplicial finite el-
ement discretizations of the Sobolev space H1
. Similarly, various finite element

  

Source: Awanou, Gerard - Department of Mathematical Sciences, Northern Illinois University

 

Collections: Mathematics