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A Weighted Least‐Squares Mixed Finite Element Formulation for Quasi‐Incompressible Elastodynamics
Author(s) -
Steeger Karl,
Schwarz Alexander,
Schröder Jörg
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110135
Subject(s) - finite element method , mixed finite element method , discretization , mathematics , compressibility , mathematical analysis , least squares function approximation , extended finite element method , norm (philosophy) , partial differential equation , physics , mechanics , structural engineering , engineering , estimator , political science , law , statistics
The purpose of this work is the application of the least‐squares finite element method to an elastodynamic, quasi‐incompressible problem under small strain assumptions. Therefore a mixed finite element based on a weighted least‐squares formulation is developed. The L 2 ‐norm minimization of the time‐discretized residuals of the given first‐order system of partial differential equations leads to a functional depending on displacements and stresses. In the numerical example the proposed mixed element is compared to an alternative approach, which is based on a least‐squares mixed finite element with improved momentum balance, see [1]. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)