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Comparison of a mixed least‐squares formulation using different approximation spaces
Author(s) -
Steeger Karl,
Schröder Jörg,
Schwarz Alexander
Publication year - 2015
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201510107
Subject(s) - mathematics , interpolation (computer graphics) , sobolev space , discretization , finite element method , least squares function approximation , mathematical analysis , function (biology) , space (punctuation) , physics , motion (physics) , statistics , estimator , linguistics , philosophy , classical mechanics , evolutionary biology , biology , thermodynamics
The main goal of the present work is the comparison of the performance of a least‐squares mixed finite element formulation where the solution variables (displacements and stresses) are interpolated using different approximation spaces. Basis for the formulation is a weak form resulting from the minimization of a least‐squares functional, compare e.g. [1]. As suitable functions for $H^1(\cal{B})$ standard interpolation polynomials of Lagrangian type are chosen. For the conforming discretization of the Sobolev space $H({\rm div}, \cal{B})$ vector‐valued Raviart‐Thomas interpolation functions, see also [2], are used. The resulting elements are named as P m P k and RT m P k . Here m (stresses) and k (displacements) denote the approximation order of the particular interpolation function. For the comparison we consider a two‐dimensional cantilever beam under plain strain conditions and small strain assumptions. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)