## The doctoral dissertations of the former Helsinki University of Technology (TKK) and Aalto University Schools of Technology (CHEM, ELEC, ENG, SCI) published in electronic format are available in the electronic publications archive of Aalto University - Aaltodoc. | |

Dissertation for the degree of Doctor of Science in Technology to be presented
with due permission of the Department of Engineering Physics and Mathematics,
for public examination and debate in Auditorium G at Helsinki University of
Technology (Espoo, Finland) on the
14^{th} of December, 2001, at 12 o'clock noon.

Overview in PDF format (ISBN 951-22-5698-3) [376 KB]

Dissertation is also available in print (ISBN 951-22-5752-1)

This thesis presents an analysis of modified finite element schemes applied to parameter dependent elliptic problems prone to locking. Two different problems of similar type are considered: the problem of anisotropic heat conduction and the thin shell problem.

This thesis consists of an overview and of the following 5 publications:

- V. Havu, J. Pitkäranta: An Analysis of Finite Element Locking in a Parameter Dependent Model Problem, Numer. Math. 89 (2001) 4, 691-714, DOI 10.1007/s002110100277. © 2001 Springer-Verlag. By permission.
- V. Havu, J. Pitkäranta: Analysis of a Bilinear Finite Element for Shallow Shells I: Approximation of Inextensional Deformations, Helsinki University of Technology, Institute of Mathematics, Research Report A430 (2000). To appear in Math. Comp. © 2000 authors & American Mathematical Society. By permission.
- V. Havu, J. Pitkäranta: Analysis of a Bilinear Element for Shallow Shells II: Consistency Error, Helsinki University of Technology, Institute of Mathematics, Research Report A433 (2001). Submitted to Math. Comp. © 2001 authors & American Mathematical Society. By permission.
- V. Havu: An Analysis of Asymptotic Consistency Error in a Parameter Dependent Model Problem, Helsinki University of Technology, Institute of Mathematics, Research Report A434 (2001). Submitted to Numer. Math. © 2001 author & Springer-Verlag. By permission.
- V. Havu, H. Hakula: An Analysis of a Bilinear Reduced Strain Element in the Case of an Elliptic Shell in a Bending Dominated State of Deformation in Advances in Computational Engineering & Sciences, Satya N. Atluri, Frederick W. Brust (eds.) (2000), pp. 732-737. © 2000 Tech Science Press. By permission.

**Keywords:**
finite elements, locking, variational crime

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© 2001 Helsinki University of Technology

Last update 2011-05-26