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Last update: Pátková Vlasta (16.11.2018)
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Last update: Pátková Vlasta (16.11.2018)
Students will learn the basics of functional analysis needed to understand finite element method. They learn to compile the variation formulation of the problem, create a discrete formula, calculate the stiffness matrix, and the right side vector. Within the seminar, each student develops three specific tasks, including a discussion of the existence and uniqueness of the solution. |
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Last update: Jahoda Milan doc. Dr. Ing. (29.11.2018)
D. Braess: Finite Elements, Cambridge University Press, 1997. S. C. Brenner, L. R. Scott: The Mathematical Theory of Finite Elements, Texts in Applied Mathematics, Vol. 15, Springer, New York, 1994. W. Hundsdorfer, J. Verwer: Numerical solution of Time-Dependent Advection-Diffusion-Reaction Equations, Springer-Verlag, Berlin, Heidelberg, 2003. V. N. Kaliakin: Introduction to Approximate Solution Techniques, Numerical Modeling,and Finite Element Methods, Marcel Dekker, Inc., New York, Basel, 2002. P. Wesseling: An Introduction to Multigrid Methods, John Wiley & Sons, 1992. |
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Last update: Pátková Vlasta (16.11.2018)
http://old.vscht.cz/mat/Info.html |
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Last update: Pátková Vlasta (16.11.2018)
Lectures and seminar. |
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Last update: Pátková Vlasta (16.11.2018)
1. Method of weighted residua. 2. Finite Element Method - Introduction. 3. Necessary minimum of functional analysis. 4. Sobolev's spaces. 5. Variational formulation of boundary value problems. 6. A simple one-dimensional boundary value problem. 7. Formulation on elements. 8. Global stiffness matrix. 9. Selected methods of numerical linear algebra. 10. Variational formulation of two and three-dimensional boundary value problems. 11. Numerical implementation. 12. Different types of elements. 13. FEM for three-dimensional problems. 14. Numerical methods for solving systems of linear algebraic equations. |
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Last update: Pátková Vlasta (16.11.2018)
Mathematics, to the same extent as Mathematics A, B. |
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Last update: Borská Lucie RNDr. Ph.D. (16.09.2019)
none |
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Last update: Pátková Vlasta (16.11.2018)
Presentation of the solution of three particular problems and discussion on the existence and uniqueness of the solution. Oral exam. |