Lamichhane, B. P., McBride, A. T. and Reddy, B. D. (2013) A finite element method for a three-field formulation of linear elasticity based on biorthogonal systems. Computer Methods in Applied Mechanics and Engineering, 258, pp. 109-117. (doi: 10.1016/j.cma.2013.02.008)
Full text not currently available from Enlighten.
Abstract
Abstract We consider a mixed finite element method based on simplicial triangulations for a three-field formulation of linear elasticity. The three-field formulation is based on three unknowns: displacement, stress and strain. In order to obtain an efficient discretization scheme, we use a pair of finite element bases forming a biorthogonal system for the strain and stress. The biorthogonality relation allows us to statically condense out the strain and stress from the saddle-point system leading to a symmetric and positive-definite system. The strain and stress can be recovered in a post-processing step simply by inverting a diagonal matrix. Moreover, we show a uniform convergence of the finite element approximation in the incompressible limit. Numerical experiments are presented to support the theoretical results.
| Item Type: | Articles |
|---|---|
| Status: | Published |
| Refereed: | Yes |
| Glasgow Author(s) Enlighten ID: | McBride, Professor Andrew |
| Authors: | Lamichhane, B. P., McBride, A. T., and Reddy, B. D. |
| College/School: | College of Science and Engineering > School of Engineering > Infrastructure and Environment |
| Journal Name: | Computer Methods in Applied Mechanics and Engineering |
| Publisher: | Elsevier |
| ISSN: | 0045-7825 |
| ISSN (Online): | 1879-2138 |
University Staff: Request a correction | Enlighten Editors: Update this record
Deposit and Record Details
Deposit and Record Details