SubjectsSubjects(version: 876)
Course, academic year 2020/2021
Advanced Methods of Applied Mathematics - AP413009
Title: Advanced Methods of Applied Mathematics
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: English
Teaching methods: full-time
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, P413009
Annotation -
Last update: Pátková Vlasta (16.11.2018)
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: 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.

Literature -
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.

Learning resources - Czech
Last update: Pátková Vlasta (16.11.2018)

Teaching methods -
Last update: Pátková Vlasta (16.11.2018)

Lectures and seminar.

Syllabus -
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.

Entry requirements -
Last update: Pátková Vlasta (16.11.2018)

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

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


Course completion requirements -
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.