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Application of the discontinuous Galerkin finite element method in small deformation regimes
Author(s) -
Bayat Hamid Reza,
Wulfinghoff Stephan,
Reese Stefanie
Publication year - 2015
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201510076
Subject(s) - discontinuous galerkin method , classification of discontinuities , finite element method , discontinuity (linguistics) , galerkin method , jump , compatibility (geochemistry) , mathematical analysis , mathematics , mechanics , physics , materials science , composite material , thermodynamics , quantum mechanics
In this paper, a finite element formulation is defined in the framework of the discontinuous Galerkin method. Discontinuous Galerkin (dG) methods are classically used in fluid mechanics, however recently their application in solid mechanics has become more vivid among scientists. Of special interest is their application in elliptic problems with constraints such as incompressibility which leads to volumetric locking phenomenon and also in some structural models of shells, plates and beams with compatibility constraints, which brings about shear locking [1]. While classical standard Galerkin methods must be continuous, dG methods can be applied for discontinuities across element boundaries, where a jump of a value (displacement) can be observed. In the present work, a dG method is applied to a linear elastic bar, where a weak discontinuity is allowed in the bar. (© 2015 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)