Title: Differential complexes and stability of finite element methods. II. The elasticity complex
Authors: Douglas N. Arnold, Richard S. Falk, and Ragnar Winther
Source: in: Compatible Spatial Discretizations,
D. Arnold, P. Bochev, R. Lehoucq, R. Nicolaides, and
M. Shashkov, eds., IMA Volumes in Mathematics and its
Applications 142, Springer Verlag 2005, pp. 47-67.
Status: Published
Abstract: A close connection between the ordinary de Rham complex
and a corresponding elasticity complex is utilized to derive new mixed
finite element methods for linear elasticity. For a formulation with
weakly imposed symmetry, this approach leads to methods which are
simpler than those previously obtained. For example, we construct
stable discretizations which use only piecewise linear elements to
approximate the stress field and piecewise constant functions to
approximate the displacement field. We also discuss how the strongly
symmetric methods proposed in [8] can be derived in the present
framework. The method of construction works in both two and three space
dimensions, but for simplicity the discussion here is limited to the
two dimensional case.
Keywords: mixed finite element method, Hellinger-Reissner principle, elasticity
Subj. class.: 65N30
URL: http://www.math.rutgers.edu/~falk/papers/elascomplexes2d.pdf