Optimal second order rectangular elasticity elements with weakly symmetric stress

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Optimal second order rectangular elasticity elements with weakly symmetric stress. / Juntunen, Mika; Lee, Jeong.

In: BIT Numerical Mathematics, Vol. 54, No. 2, 2014, p. 425-445.

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Juntunen, Mika ; Lee, Jeong. / Optimal second order rectangular elasticity elements with weakly symmetric stress. In: BIT Numerical Mathematics. 2014 ; Vol. 54, No. 2. pp. 425-445.

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@article{5ae96269c7574c279a6132b951490caa,
title = "Optimal second order rectangular elasticity elements with weakly symmetric stress",
abstract = "We present new second order rectangular mixed finite elements for linear elasticity where the symmetry condition on the stress is imposed weakly with a Lagrange multiplier. The key idea in constructing the new finite elements is enhancing the stress space of the Awanou's rectangular elements (rectangular Arnold-Falk-Winther elements) using bubble functions. The proposed elements have only 18 and 63 degrees of freedom for the stress in two and three dimensions, respectively, and they achieve the optimal second order convergence of errors for all the unknowns. We also present a new simple a priori error analysis and provide numerical results illustrating our analysis.",
keywords = "Elasticity, Mixed finite element, Rectangular finite element, Weakly imposed symmetry",
author = "Mika Juntunen and Jeong Lee",
year = "2014",
doi = "10.1007/s10543-013-0460-2",
language = "English",
volume = "54",
pages = "425--445",
journal = "BIT - Numerical Mathematics",
issn = "0006-3835",
publisher = "Springer Netherlands",
number = "2",

}

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TY - JOUR

T1 - Optimal second order rectangular elasticity elements with weakly symmetric stress

AU - Juntunen, Mika

AU - Lee, Jeong

PY - 2014

Y1 - 2014

N2 - We present new second order rectangular mixed finite elements for linear elasticity where the symmetry condition on the stress is imposed weakly with a Lagrange multiplier. The key idea in constructing the new finite elements is enhancing the stress space of the Awanou's rectangular elements (rectangular Arnold-Falk-Winther elements) using bubble functions. The proposed elements have only 18 and 63 degrees of freedom for the stress in two and three dimensions, respectively, and they achieve the optimal second order convergence of errors for all the unknowns. We also present a new simple a priori error analysis and provide numerical results illustrating our analysis.

AB - We present new second order rectangular mixed finite elements for linear elasticity where the symmetry condition on the stress is imposed weakly with a Lagrange multiplier. The key idea in constructing the new finite elements is enhancing the stress space of the Awanou's rectangular elements (rectangular Arnold-Falk-Winther elements) using bubble functions. The proposed elements have only 18 and 63 degrees of freedom for the stress in two and three dimensions, respectively, and they achieve the optimal second order convergence of errors for all the unknowns. We also present a new simple a priori error analysis and provide numerical results illustrating our analysis.

KW - Elasticity

KW - Mixed finite element

KW - Rectangular finite element

KW - Weakly imposed symmetry

UR - http://www.scopus.com/inward/record.url?scp=84902800571&partnerID=8YFLogxK

U2 - 10.1007/s10543-013-0460-2

DO - 10.1007/s10543-013-0460-2

M3 - Article

VL - 54

SP - 425

EP - 445

JO - BIT - Numerical Mathematics

JF - BIT - Numerical Mathematics

SN - 0006-3835

IS - 2

ER -

ID: 9431521