Uniformly convergent interior penalty methods using multilinear approximations for problems in elasticity

Grieshaber, B.J., McBride, A.T. and Reddy, B.D. (2015) Uniformly convergent interior penalty methods using multilinear approximations for problems in elasticity. SIAM: Journal on Numerical Analysis, 53(5), pp. 2255-2278. (doi:10.1137/140966253)

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Abstract

Interior penalty methods for linear elasticity, when used with bilinear elements, are effective in the context of compressible materials. However, they may produce poor approximations with these elements in the nearly incompressible regime. We propose a new general interior penalty formulation and prove that it is uniformly convergent with respect to the compressibility parameter for multilinear elements. The new formulation is a modification of well-known methods (nonsymmetric, incomplete, and symmetric interior penalty Galerkin) through underintegration of selected edge terms.

Item Type:Articles
Additional Information:The research of the authors was funded by the National Research Foundation, through the South African Research Chair in Computational Mechanics.
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:McBride, Dr Andrew
Authors: Grieshaber, B.J., McBride, A.T., and Reddy, B.D.
College/School:College of Science and Engineering > School of Engineering > Infrastructure and Environment
Journal Name:SIAM: Journal on Numerical Analysis
Publisher:Society for Industrial and Applied Mathematics
ISSN:0036-1429
ISSN (Online):1095-7170

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