|
|
|
||
Last update: Janovská Drahoslava prof. RNDr. CSc. (24.09.2018)
|
|
||
Last update: Janovská Drahoslava prof. RNDr. CSc. (25.09.2018)
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. |
|
||
Last update: Janovská Drahoslava prof. RNDr. CSc. (25.09.2018)
1. D. Braess: Finite Elements, Cambridge University Press, 1997. 2. S. C. Brenner, L. R. Scott: The Mathematical Theory of Finite Elements, Texts in Applied Mathematics, Vol. 15, Springer, New York, 1994. 3. W. Hundsdorfer, J. Verwer: Numerical solution of Time-Dependent Advection-Diffusion-Reaction Equations, Springer-Verlag, Berlin, Heidelberg, 2003. 4. D. Janovská: Stručně o metodě konečných prvků. Sborník prací ze semináře ”Reakční a transportní jevy II”, Konopiště 8.–11.6.2007, ed. M. Marek, I. Schreiber, L. Schreiberová, Vydavatelství VŠCHT, Praha, 2007, pp. 46–60. 5. V. N. Kaliakin: Introduction to Approximate Solution Techniques, Numerical Modeling,and Finite Element Methods, Marcel Dekker, Inc., New York, Basel, 2002. 6. M. Kubíček, M. Dubcová, D. Janovská: Numerické metody a algoritmy, skripta VŠCHT, 2. vydání, 2005. 7. P. Wesseling: An Introduction to Multigrid Methods, John Wiley & Sons, 1992. 8. L. Zajíček: Vybrané úlohy z matematické analýzy, Matfyzpress, Praha, 2002. |
|
||
Last update: Janovská Drahoslava prof. RNDr. CSc. (25.09.2018)
http://old.vscht.cz/mat/Info.html |
|
||
Last update: Janovská Drahoslava prof. RNDr. CSc. (25.09.2018)
Lectures and seminar. |
|
||
Last update: Janovská Drahoslava prof. RNDr. CSc. (25.09.2018)
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. |
|
||
Last update: Janovská Drahoslava prof. RNDr. CSc. (25.09.2018)
Mathematics, to the same extent as Mathematics A, B. |
|
||
Last update: Borská Lucie RNDr. Ph.D. (16.09.2019)
none |
|
||
Last update: Janovská Drahoslava prof. RNDr. CSc. (25.09.2018)
Presentation of the solution of three particular problems and discussion on the existence and uniqueness of the solution. Oral exam. |