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Efficient linear and nonlinear heat conduction with a quadrilateral elementA method is presented for performing efficient and stable finite element calculations of heat conduction with quadrilaterals using one-point quadrature. The stability in space is obtained by using a stabilization matrix which is orthogonal to all linear fields and its magnitude is determined by a stabilization parameter. It is shown that the accuracy is almost independent of the value of the stabilization parameter over a wide range of values; in fact, the values 3, 2 and 1 for the normalized stabilization parameter lead to the 5-point finite difference, 9-point finite difference and fully integrated finite element operators, respectively, for rectangular meshes; numerical experiments reported here show that the three have identical rates of convergence in the L2 norm. Eigenvalues of the element matrices, which are needed for stability limits, are also given. Numerical applications are used to show that the method yields accurate solutions with large increases in efficiency, particularly in nonlinear problems.
Document ID
19840055674
Acquisition Source
Legacy CDMS
Document Type
Reprint (Version printed in journal)
External Source(s)
Authors
Liu, W. K.
(Northwestern Univ. Evanston, IL, United States)
Belytschko, T.
(Northwestern University Evanston, IL, United States)
Date Acquired
August 12, 2013
Publication Date
May 1, 1984
Publication Information
Publication: International Journal for Numerical Methods in Engineering
Volume: 20
ISSN: 0029-5981
Subject Category
Fluid Mechanics And Heat Transfer
Accession Number
84A38461
Funding Number(s)
CONTRACT_GRANT: F49620-82-K-0013
CONTRACT_GRANT: NAG1-210
Distribution Limits
Public
Copyright
Other

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