# 470-4505/03 – Numerical Methods III (NM3)

 Gurantor department Department of Applied Mathematics Credits 6 Subject guarantor doc. Ing. Dalibor Lukáš, Ph.D. Subject version guarantor doc. Ing. Dalibor Lukáš, Ph.D. Study level undergraduate or graduate Requirement Optional Year 2 Semester winter Study language Czech Year of introduction 2019/2020 Year of cancellation Intended for the faculties FEI Intended for study types Follow-up Master
Instruction secured by
BAI0012 Ing. Michaela Bailová
LUK76 doc. Ing. Dalibor Lukáš, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 2+2
Part-time Credit and Examination 10+10

### Subject aims expressed by acquired skills and competences

The aim of the course is to introduce advanced topis of numerical analysis for partial differential equations. In the first part we shall deal with mathematical modelling in elasticity, the other part treats fluid dynamics. Both parts start with deriving a mathematical model from physical principles. Then variational formulations are introduced, which are solved by the finite element method afterwards.

Lectures
Tutorials
Project work

### Summary

In the first part of the course we shall deal with mathematical modelling in elasticity, the other part treats fluid dynamics. Both parts start with deriving a mathematical model from physical principles. Then variational formulations are introduced, which are solved by the finite element method afterwards.

### Compulsory literature:

Braess, D.: Finite elements. Cambridge University Press, 2001 Feistauer, M.: Theory and numerics for problems of fluid dynamics. MATFYZ UK Praha, 2006

### Recommended literature:

Quarteroni, A., Valli, A.: Numerical approximation of PDEs. Springer, 2008.

### Way of continuous check of knowledge in the course of semester

Test and project.

### Other requirements

Knowledge about numerical and variational methods

### Prerequisities

Subject has no prerequisities.

### Co-requisities

Subject has no co-requisities.

### Subject syllabus:

Lectures: 1. Elasticity - kinematics 2. Elasticity - equilibrium 3. Elasticity - constitutive laws, Hooke's law 4. Elasticity - displacement variational formulation 5. Elasticity - Korn's inequalities, finite element method 6. Elasticity - mixed formulations, locking effect 7. Fluid dynamics - physical properties of fluids 8. Fluid dynamics - kinematics 9. Fluid dynamics - Stokes and Navier-Stokes equations 10. Fluid dynamics - variational formulation 11. Fluid dynamics - finite element method 12. Fluid dynamics - apriori and aposteriori error estimates 13. Fluid dynamics - singularities 14. Fluid dynamics - numerical stability Exercises: 1. Elasticity - kinematics 2. Elasticity - equilibrium 3. Elasticity - constitutive laws, Hooke's law 4. Elasticity - displacement variational formulation 5. Elasticity - Korn's inequalities, finite element method 6. Elasticity - mixed formulations, locking effect 7. Fluid dynamics - physical properties of fluids 8. Fluid dynamics - kinematics 9. Fluid dynamics - Stokes and Navier-Stokes equations 10. Fluid dynamics - variational formulation 11. Fluid dynamics - finite element method 12. Fluid dynamics - apriori and aposteriori error estimates 13. Fluid dynamics - singularities 14. Fluid dynamics - numerical stability Projects: Finite element method for a fluid dynamic problem. Finite element method for an elasticity problem.

### Conditions for subject completion

Full-time form (validity from: 2019/2020 Winter semester)
Task nameType of taskMax. number of points
Min. number of points
Credit and Examination Credit and Examination 100 (100) 51
Credit Credit 30  15
Examination Examination 70  21
Mandatory attendence parzicipation: bude doplněno

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### Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2021/2022 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics P Czech Ostrava 2 Optional study plan
2021/2022 (N0541A170007) Computational and Applied Mathematics (S02) Computational Methods and HPC K Czech Ostrava 2 Optional study plan
2021/2022 (N0541A170007) Computational and Applied Mathematics (S02) Computational Methods and HPC P Czech Ostrava 2 Optional study plan
2021/2022 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics K Czech Ostrava 2 Optional study plan
2020/2021 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics K Czech Ostrava 2 Optional study plan
2020/2021 (N0541A170007) Computational and Applied Mathematics (S02) Computational Methods and HPC P Czech Ostrava 2 Optional study plan
2020/2021 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics P Czech Ostrava 2 Optional study plan
2020/2021 (N0541A170007) Computational and Applied Mathematics (S02) Computational Methods and HPC K Czech Ostrava 2 Optional study plan
2019/2020 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics P Czech Ostrava 2 Optional study plan
2019/2020 (N0541A170007) Computational and Applied Mathematics (S02) Computational Methods and HPC P Czech Ostrava 2 Optional study plan
2019/2020 (N0541A170007) Computational and Applied Mathematics (S01) Applied Mathematics K Czech Ostrava 2 Optional study plan
2019/2020 (N0541A170007) Computational and Applied Mathematics (S02) Computational Methods and HPC K Czech Ostrava 2 Optional study plan

### Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner