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Our aim is to fill gaps in knowledge of students, namely in the field of Functional Analysis, in such a way that they will be able to understand the mathematical features of the Finite Element Method. The Finite Element Method is a modern numerical method that enables us to approximate continuously the solution of partial differentia equations. Students will also try to apply the method (including software) for solving particular simple problems.
Last update: Janovská Drahoslava (29.08.2013)
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Students will get acquainted with mathematical principles of methods that continuously approximate the solution of partial differential equations, in particular they will study the method of weighted residuals and the Finite Element Method.
Last update: Janovská Drahoslava (29.08.2013)
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R: Kubíček Milan, Dubcová Miroslava, Janovská Drahoslava: Numerické metody a algoritmy, VŠCHT Praha, 2005 (druhé vydání).
A: Suli Endre: Lecture notes of Finite Element Method for Partial Differential Equations, http://people.maths.ox.ac.uk/suli/fem.pdf Last update: Janovská Drahoslava (29.08.2013)
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Lectures and seminars, each student solves 3 small project and presents them in seminars.
Last update: Janovská Drahoslava (29.08.2013)
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1. The method of weighted residuals. 2. Introduction to the Finite Element Method. 3. Short introduction to the Functional Analysis 4. Sobolev Spaces 5. Variational formulation of the boundary problems. 6. A simple one dimensional example. 7. Element point of wiev. 8. Global stiffness and mass matrix. 9. Selected methods of the Numerical Linear Algebra. 10. Variational formulation of the boundary problems in two and three dimensions. 11. Numerical realization. 12. Different types of elements. 13. The finite element method for three dimensional problems. 14. Numerical solution of systems of linear algebraic equations.
Last update: Janovská Drahoslava (29.08.2013)
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http://www.vscht.cz/mat/MAM/FEM_UM.pdf http://www.vscht.cz/mat/Ang/NM-Ang/e_nm_semin.html Suli Endre: Lecture notes of Finite Element Method for Partial Differential Equations, http://people.maths.ox.ac.uk/suli/fem.pdf Last update: TAJ413 (05.09.2013)
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Basic course MI and MII, the advantage is also passing the course on Numerical Methods and the course MIII. Last update: Janovská Drahoslava (29.08.2013)
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| Teaching methods | ||||
| Activity | Credits | Hours | ||
| Účast na přednáškách | 1 | 28 | ||
| Práce na individuálním projektu | 1.5 | 42 | ||
| Příprava na zkoušku a její absolvování | 1 | 28 | ||
| Účast na seminářích | 0.5 | 14 | ||
| 4 / 4 | 112 / 112 | |||
| Coursework assessment | |
| Form | Significance |
| Regular attendance | 20 |
| Defense of an individual project | 20 |
| Report from individual projects | 40 |
| Oral examination | 20 |