SubjectsSubjects(version: 853)
Course, academic year 2019/2020
  
Advanced Methods of Applied Mathematics - P413009
Title: Moderní metody aplikované matematiky
Guaranteed by: Department of Mathematics (413)
Actual: from 2019
Semester: both
Points: 0
E-Credits: 0
Examination process:
Hours per week, examination: 3/0 other [hours/week]
Capacity: winter:unknown / unknown (unknown)
summer:unknown / unknown (unknown)
Min. number of students: unlimited
Language: Czech
Teaching methods: full-time
Level:  
For type: doctoral
Note: course is intended for doctoral students only
can be fulfilled in the future
you can enroll for the course in winter and in summer semester
Guarantor: Janovská Drahoslava prof. RNDr. CSc.
Červená Lenka RNDr. Ph.D.
Interchangeability : D413028
Is interchangeable with: AP413009
Annotation -
Last update: Janovská Drahoslava prof. RNDr. CSc. (24.09.2018)
The aim of the course is to supplement the students' knowledge especially in the field of functional analysis in order to understand the mathematical fundamentals of the finite element method. The finite element method is an advanced numerical method that allows continuous approximation of solutions of partial differential equations.
Aim of the course -
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.

Literature -
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.

Learning resources -
Last update: Janovská Drahoslava prof. RNDr. CSc. (25.09.2018)

http://old.vscht.cz/mat/Info.html

Teaching methods -
Last update: Janovská Drahoslava prof. RNDr. CSc. (25.09.2018)

Lectures and seminar.

Syllabus -
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.

Entry requirements -
Last update: Janovská Drahoslava prof. RNDr. CSc. (25.09.2018)

Mathematics, to the same extent as Mathematics A, B.

Registration requirements -
Last update: Borská Lucie RNDr. Ph.D. (16.09.2019)

none

Course completion requirements -
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.

Coursework assessment
Form Significance
Defense of an individual project 50
Oral examination 50

 
VŠCHT Praha