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.
Aalto

Finite Element Methods for Parameter Dependent Problems

Mika Juntunen

Dissertation for the degree of Doctor of Science in Technology to be presented with due permission of the Faculty of Information and Natural Sciences for public examination and debate in Auditorium E at Helsinki University of Technology (Espoo, Finland) on the 5th of August, 2009, at 12 noon.

Overview in PDF format (ISBN 978-951-22-9994-2)   [155 KB]
Dissertation is also available in print (ISBN 978-951-22-9993-5)

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.

This thesis consists of an overview and of the following 6 publications:

  1. Mika Juntunen and Rolf Stenberg. 2008. On a mixed discontinuous Galerkin method. Electronic Transactions on Numerical Analysis, volume 32, pages 17-32.
  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.
  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.
  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.
  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.
  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.

Keywords: finite element method, boundary conditions, Nitsche's method, a posteriori estimation, Stokes equation, Darcy equation, Brinkman equation

This publication is copyrighted. You may download, display and print it for Your own personal use. Commercial use is prohibited.

© 2009 Helsinki University of Technology

Last update 2011-05-26