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 | 2022/2023 |

Intended for the faculties | FEI | Intended for study types | Follow-up Master |

Instruction secured by | |||
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Login | Name | Tuitor | Teacher giving lectures |

BAI0012 | Ing. Michaela Bailová, Ph.D. | ||

LUK76 | doc. Ing. Dalibor Lukáš, Ph.D. |

Extent of instruction for forms of study | ||
---|---|---|

Form of study | Way of compl. | Extent |

Full-time | Credit and Examination | 2+2 |

Part-time | Credit and Examination | 10+10 |

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

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.

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

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

Test and project.

Knowledge about numerical and variational methods

Subject has no prerequisities.

Subject has no co-requisities.

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.

Task name | Type of task | Max. number of points
(act. for subtasks) | Min. number of points | Max. počet pokusů |
---|---|---|---|---|

Credit and Examination | Credit and Examination | 100 (100) | 51 | |

Credit | Credit | 30 | 15 | |

Examination | Examination | 70 | 21 | 3 |

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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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Academic year | Programme | Branch/spec. | Spec. | Zaměření | Form | Study language | Tut. centre | Year | W | S | Type of duty | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

2022/2023 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | K | Czech | Ostrava | 2 | Optional | study plan | ||||

2022/2023 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | P | Czech | Ostrava | 2 | Optional | study plan | ||||

2022/2023 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | K | Czech | Ostrava | 2 | Optional | study plan | ||||

2022/2023 | (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 | 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 |

Block name | Academic year | Form of study | Study language | Year | W | S | Type of block | Block owner |
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