470-4505/01 – 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 | 2015/2016 | Year of cancellation | 2020/2021 |
Intended for the faculties | FEI | Intended for study types | Follow-up Master |
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.
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
Occurrence in study plans
Occurrence in special blocks
Assessment of instruction