| Course Unit Code | 470-4505/03 |
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| Number of ECTS Credits Allocated | 6 ECTS credits |
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| Type of Course Unit * | Optional |
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| Level of Course Unit * | Second Cycle |
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| Year of Study * | Second Year |
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| Semester when the Course Unit is delivered | Winter Semester |
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| Mode of Delivery | Face-to-face |
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| Language of Instruction | Czech |
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| Prerequisites and Co-Requisites | Course succeeds to compulsory courses of previous semester |
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| Name of Lecturer(s) | Personal ID | Name |
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| LUK76 | doc. Ing. Dalibor Lukáš, Ph.D. |
| Summary |
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| 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. |
| Learning Outcomes of the Course Unit |
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| 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. |
| Course Contents |
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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. |
| Recommended or Required Reading |
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| Required Reading: |
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Braess, D.: Finite elements. Cambridge University Press, 2001
Feistauer, M.: Theory and numerics for problems of fluid dynamics. MATFYZ UK Praha, 2006 |
Braess, D.: Finite elements. Cambridge University Press, 2001
Feistauer, M.: Theory and numerics for problems of fluid dynamics. MATFYZ UK Praha, 2006 |
| Recommended Reading: |
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| Quarteroni, A., Valli, A.: Numerical approximation of PDEs. Springer, 2008. |
| Quarteroni, A., Valli, A.: Numerical approximation of PDEs. Springer, 2008. |
| Planned learning activities and teaching methods |
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| Lectures, Tutorials, Project work |
| Assesment methods and criteria |
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| Task Title | Task Type | Maximum Number of Points
(Act. for Subtasks) | Minimum Number of Points for Task Passing |
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| Credit and Examination | Credit and Examination | 100 (100) | 51 |
| Credit | Credit | 30 | 15 |
| Examination | Examination | 70 | 21 |