Terminated in academic year 2022/2023

Numerical Methods III

Type of study	Follow-up Master
Language of instruction	Czech
Code	470-4505/03
Abbreviation	NM3
Course title	Numerical Methods III
Credits	6
Coordinating department	Department of Applied Mathematics
Course coordinator	doc. Ing. Dalibor Lukáš, Ph.D.

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.

Literature

Braess, D.: Finite elements. Cambridge University Press, 2001

Feistauer, M.: Theory and numerics for problems of fluid dynamics. MATFYZ UK Praha, 2006

Advised literature

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

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