470-4505/04 – Numerical Methods III (NM3)

Gurantor departmentDepartment of Applied MathematicsCredits6
Subject guarantordoc. Ing. Dalibor Lukáš, Ph.D.Subject version guarantordoc. Ing. Dalibor Lukáš, Ph.D.
Study levelundergraduate or graduateRequirementOptional
Year2Semesterwinter
Study languageEnglish
Year of introduction2019/2020Year of cancellation2022/2023
Intended for the facultiesFEIIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
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.

Teaching methods

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.

Additional study materials

Way of continuous check of knowledge in the course of semester

Test and project.

E-learning

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, validity until: 2022/2023 Summer semester)
Task nameType of taskMax. number of points
(act. for subtasks)		Min. number of pointsMax. počet pokusů
Credit and Examination Credit and Examination 100 (100) 51
        Credit Credit 30  15
        Examination Examination 70  21 3
Mandatory attendence participation: Participation in lectures and seminars is governed by the study and examination regulations.

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Conditions for subject completion and attendance at the exercises within ISP: Completion of all mandatory tasks within individually agreed deadlines.

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Occurrence in study plans

Academic yearProgrammeBranch/spec.Spec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2022/2023 (N0541A170008) Computational and Applied Mathematics (S01) Applied Mathematics P English Ostrava 2 Optional study plan
2022/2023 (N0541A170008) Computational and Applied Mathematics (S02) Computational Methods and HPC P English Ostrava 2 Optional study plan
2021/2022 (N0541A170008) Computational and Applied Mathematics (S01) Applied Mathematics P English Ostrava 2 Optional study plan
2021/2022 (N0541A170008) Computational and Applied Mathematics (S02) Computational Methods and HPC P English Ostrava 2 Optional study plan
2020/2021 (N0541A170008) Computational and Applied Mathematics (S02) Computational Methods and HPC P English Ostrava 2 Optional study plan
2020/2021 (N0541A170008) Computational and Applied Mathematics (S01) Applied Mathematics P English Ostrava 2 Optional study plan
2019/2020 (N0541A170008) Computational and Applied Mathematics (S01) Applied Mathematics P English Ostrava 2 Compulsory study plan
2019/2020 (N0541A170008) Computational and Applied Mathematics (S02) Computational Methods and HPC P English Ostrava 2 Optional study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

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