Finite element methods for parameter dependent problems

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dc.contributor Aalto-yliopisto fi
dc.contributor Aalto University en
dc.contributor.author Juntunen, Mika
dc.date.accessioned 2012-08-23T05:27:30Z
dc.date.available 2012-08-23T05:27:30Z
dc.date.issued 2009
dc.identifier.isbn 978-951-22-9994-2
dc.identifier.isbn 978-951-22-9993-5 (printed) #8195;
dc.identifier.issn 1797-5867
dc.identifier.uri https://aaltodoc.aalto.fi/handle/123456789/4635
dc.description.abstract This thesis develops finite element methods for parameter dependent equations. The interest lies in cases where the nature of the problem and the numerical methods used change with the parameters. The studied examples are the reaction-diffusion problem, the Robin boundary condition, which generalizes the Dirichlet and Neumann conditions, and the Brinkman equation, which generalizes the Stokes and the Darcy equations. The developed methods depend continuously on the problem parameters and work even for the limiting values. A posteriori estimates are derived for all the proposed methods, taking into account the parameters. Significant parts of this work are the implementation of the proposed methods and the numerical verfication of the developed theory. en
dc.format.extent Verkkokirja (155 KB, 14 s.)
dc.format.mimetype application/pdf
dc.language.iso en en
dc.publisher Teknillinen korkeakoulu en
dc.relation.ispartofseries Research reports / Helsinki University of Technology, Institute of Mathematics. A, 573 en
dc.relation.haspart [Publication 1]: Mika Juntunen and Rolf Stenberg. 2008. On a mixed discontinuous Galerkin method. Electronic Transactions on Numerical Analysis, volume 32, pages 17-32. en
dc.relation.haspart [Publication 2]: Mika Juntunen and Rolf Stenberg. 2009. Nitsche's method for general boundary conditions. Mathematics of Computation, volume 78, number 267, pages 1353-1374. doi:10.1090/S0025-5718-08-02183-2. © 2009 American Mathematical Society (AMS). By permission. en
dc.relation.haspart [Publication 3]: P. Hansbo and M. Juntunen. 2009. Weakly imposed Dirichlet boundary conditions for the Brinkman model of porous media flow. Applied Numerical Mathematics, volume 59, number 6, pages 1274-1289. doi:10.1016/j.apnum.2008.07.003. © 2009 Elsevier Science. By permission. en
dc.relation.haspart [Publication 4]: Mika Juntunen and Rolf Stenberg. 2009. A residual based a posteriori estimator for the reaction-diffusion problem. Comptes Rendus Mathematique, volume 347, numbers 9-10, pages 555-558. doi:10.1016/j.crma.2009.03.010. en
dc.relation.haspart [Publication 5]: Mika Juntunen and Rolf Stenberg. 2009. Analysis of finite element methods for the Brinkman problem. Espoo, Finland. 19 pages. Helsinki University of Technology Institute of Mathematics Research Reports, A557. © 2009 by authors. en
dc.relation.haspart [Publication 6]: Antti Hannukainen, Mika Juntunen, and Rolf Stenberg. 2009. Computations with finite element methods for the Brinkman problem. Espoo, Finland. 19 pages. Helsinki University of Technology Institute of Mathematics Research Reports, A569. © 2009 by authors. en
dc.subject.other Mathematics en
dc.title Finite element methods for parameter dependent problems en
dc.type G5 Artikkeliväitöskirja fi
dc.contributor.department Matematiikan ja systeemianalyysin laitos fi
dc.subject.keyword finite element methods en
dc.subject.keyword boundary conditions en
dc.subject.keyword Nitsche's method en
dc.subject.keyword a posteriori estimation en
dc.subject.keyword Stokes equation en
dc.subject.keyword Darcy equation en
dc.subject.keyword Brinkman equation en
dc.identifier.urn URN:ISBN:978-951-22-9994-2
dc.type.dcmitype text en
dc.type.ontasot Väitöskirja (artikkeli) fi
dc.type.ontasot Doctoral dissertation (article-based) en


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