A Stabilized Low Order Finite Element Method for Three Dimensional Elasticity Problems

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We introduce a low order finite element method for three dimensional elasticity problems. We extend Kouhia-Stenberg element [12] by using two nonconforming components and one conforming component, adding stabilizing terms on the associated bilinear form to ensure the discrete Korn's inequality. Using the second Strang's lemma, we show that our scheme has optimal convergence rates in L-2 and piecewise H-1-norms even when Poisson ratio nu approaches 1/2. Even though some efforts have been made to design a low order method for three dimensional problems in [11, 16], their method uses some higher degree basis functions. Our scheme is the first true low order method. We provide three numerical examples which support our analysis. We compute two examples having analytic solutions. We observe the optimal L-2 and H-1 errors for many different choice of Poisson ratios including the nearly incompressible cases. In the last example, we simulate the driven cavity problem. Our scheme shows non-locking phenomena for the driven cavity problems also.
Publisher
GLOBAL SCIENCE PRESS
Issue Date
2020-05
Language
English
Article Type
Article
Citation

NUMERICAL MATHEMATICS-THEORY METHODS AND APPLICATIONS, v.13, no.2, pp.281 - 295

ISSN
1004-8979
DOI
10.4208/nmtma.OA-2019-0034
URI
http://hdl.handle.net/10203/273739
Appears in Collection
MA-Journal Papers(저널논문)
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