Analysis of reduced finite element schemes in parameter dependent elliptic problems
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Doctoral thesis (article-based)
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Research reports / Helsinki University of Technology, Institute of Mathematics. A, 442
AbstractThis 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.
finite elements, locking, variational crime
- 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. [article1.pdf] © 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. [article2.pdf] © 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. [article3.pdf] © 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. [article4.pdf] © 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. [article5.pdf] © 2000 Tech Science Press. By permission.