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Discontinuous Galerkin and the Crouzeix-Raviart element : Application to elasticity
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- Hansbo, Peter (author)
- Jönköping University,JTH. Forskningsmiljö Produktutveckling - Simulering och optimering,Chalmers tekniska högskola,Chalmers University of Technology
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- Larson, Mats G (author)
- Chalmers University of Technology,Chalmers tekniska högskola
- Jönköping University JTH Forskningsmiljö Produktutveckling - Simulering och optimering (creator_code:org_t)
- 2003-03-15
- 2003
- English.
- In: Mathematical Modelling and Numerical Analysis. - : EDP Sciences. - 0764-583X .- 1290-3841. ; 37:1, s. 63-72
- Journal article (peer-reviewed)
Abstract
Subject headings
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- We propose a discontinuous Galerkin method for linear elasticity, based on discontinuous piecewise linear approximation of the displacements. We show optimal order a priori error estimates, uniform in the incompressible limit, and thus locking is avoided. The discontinuous Galerkin method is closely related to the non-conforming Crouzeix-Raviart (CR) element, which in fact is obtained when one of the stabilizing parameters tends to infinity. In the case of the elasticity operator, for which the CR element is not stable in that it does not fulfill a discrete Korn's inequality, the discontinuous framework naturally suggests the appearance of (weakly consistent) stabilization terms. Thus, a stabilized version of the CR element, which does not lock, can be used for both compressible and ( nearly) incompressible elasticity. Numerical results supporting these assertions are included. The analysis directly extends to higher order elements and three spatial dimensions.
Subject headings
- TEKNIK OCH TEKNOLOGIER -- Maskinteknik -- Teknisk mekanik (hsv//swe)
- ENGINEERING AND TECHNOLOGY -- Mechanical Engineering -- Applied Mechanics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Keyword
- Crouzeix-Raviart element
- Nitsche's method
- discontinuous Galerkin
- incompressible elasticity
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- ref (subject category)
- art (subject category)
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