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MATHEMATICS OF COMPUTATION Volume 77, Number 263, July 2008, Pages 12291251
 

Summary: MATHEMATICS OF COMPUTATION
Volume 77, Number 263, July 2008, Pages 1229­1251
S 0025-5718(08)02071-1
Article electronically published on January 29, 2008
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

  

Source: Arnold, Douglas N. - School of Mathematics, University of Minnesota

 

Collections: Mathematics