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A stress‐velocity least‐squares mixed finite element formulation for incompressible elastodynamics
Author(s) -
Nisters Carina,
Schwarz Alexander,
Steeger Karl,
Schröder Jörg
Publication year - 2015
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201510099
Subject(s) - discretization , finite element method , weighting , mathematics , compressibility , mathematical analysis , norm (philosophy) , scalar (mathematics) , dependency (uml) , mixed finite element method , constitutive equation , least squares function approximation , physics , mechanics , geometry , computer science , law , software engineering , political science , acoustics , thermodynamics , statistics , estimator
In the framework of solving elastodynamic problems using a least‐squares mixed finite element method (LSFEM) the implementation of a stress‐velocity formulation for small strains is introduced and discussed in the present contribution. The element formulation is based on a first‐order div – grad system, with the balance equation of momentum and the constitutive law as the governing equations. Application of the L 2 ‐norm to the two residuals leads to a functional depending on stresses and velocities. Different time discretization schemes are considered, a scalar weighting is introduced and chosen in dependency of the different time discretization methods. In a numerical example the influence of the time integration method, the chosen time step width and the related weighing factor are investigated for a two‐dimensional problem. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)