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A Least‐Squares Mixed Finite Element for Quasi‐Incompressible Elastodynamics
Author(s) -
Schwarz Alexander,
Steeger Karl,
Schröder Jörg
Publication year - 2010
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201010102
Subject(s) - finite element method , compressibility , mathematics , discretization , mathematical analysis , mixed finite element method , norm (philosophy) , elasticity (physics) , least squares function approximation , extended finite element method , element (criminal law) , physics , mechanics , structural engineering , engineering , statistics , estimator , political science , law , thermodynamics
In the present work, a mixed finite element based on a modified least‐squares formulation is proposed. Here, we consider the time‐dependent equations for quasi‐incompressible elastodynamics under small strain assumptions. The main goal is to obtain an accurate approximation of both displacements and stresses in particular for the lowest‐order element. Basis for the element formulation is a weak form resulting from a least‐squares method. The L 2 ‐norm minimization of the time‐discretized residuals of the given first‐order system leads to a functional depending on approximations for displacements and stresses. By introducing a time‐independent displacement test function, a weak form is derived. A numerical example concerning quasi‐incompressible elasticity shows the performance of the approach for the lowest‐order element RT 0 P 1 as . (© 2010 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)