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 | Compulsory |

Year | 1 | Semester | summer |

Study language | Czech | ||

Year of introduction | 2010/2011 | Year of cancellation | |

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

Instruction secured by | |||
---|---|---|---|

Login | Name | Tuitor | Teacher giving lectures |

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 course will introduce students to the basic principles of formulation of boundary and initial value problems and mathematical derivation of the finite element method. An attention is also paid to the computer implementation and analysis of the accuracy of the method.
Theoretical foundations provide qualified assessment of the results obtained by the available software tools as well as a further development of the finite element methods.

Lectures

Tutorials

The course deals with a description of the finite element method and its use for solving boundary and initial value problems arising in mathematical modeling of physical processes, such as problems of heat conduction, elasticity etc.

K. Rektorys:. Variational Methods in Mathematics, Science and Engineering, D. Reidel Publ. Comp, NY 1975

C. Johnson: Numerical solution of partial differential equations by the finite element method, Cambridge Univ. Press, 1995

There are not defined other requirements for student.

Subject has no prerequisities.

Subject has no co-requisities.

Lectures:
Mathematical formulations of boundary and initial value problems describing physical phenomena. Advantages of mathematical modeling and correct use of mathematical models.
Mathematical formulations of 2D and 3D problems.
Variational (weak) formulations. Energy functional and formulations. Existence and regularity of solutions.
Ritz-Galerkin method.
Finite element method in 1D.
Finite element method in 2D and 3D.
Programming of FEM.
Reference element. Isoparameteric finite elements.
FEM error. Apriori estimates.
Aposteriori estimates. Adaptive methods, optimal grids.
Nonconform and mixed methods. Nonlinear problems.
Tutorials:
Derivation of mathematical formulations of boundary and initial value problems for various physical phenomena.
Variational (weak) formulations.
Use of Ritz-Galerkin method.
FEM algorithm.
Programming, pre and postprocessing.
Solution to selected problems, discretization error.
Use of commercial software.
Projects:
Projects consist of a series of simple problems, the solution to which makes use of the theory. Projects may be concerned with programming of FEM.

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

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

Exercises evaluation | 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 | |
---|---|---|---|---|---|---|---|---|---|---|---|---|

2024/2025 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | NMS | K | Czech | Ostrava | 1 | Compulsory | study plan | |||

2024/2025 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | NMS | P | Czech | Ostrava | 1 | Compulsory | study plan | |||

2024/2025 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | VM | P | Czech | Ostrava | 1 | Compulsory | study plan | |||

2024/2025 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | VM | K | Czech | Ostrava | 1 | Compulsory | study plan | |||

2023/2024 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | NMS | P | Czech | Ostrava | 1 | Compulsory | study plan | |||

2023/2024 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | NMS | K | Czech | Ostrava | 1 | Compulsory | study plan | |||

2023/2024 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | VM | P | Czech | Ostrava | 1 | Compulsory | study plan | |||

2023/2024 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | VM | K | Czech | Ostrava | 1 | Compulsory | study plan | |||

2022/2023 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | NMS | K | Czech | Ostrava | 1 | Compulsory | study plan | |||

2022/2023 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | NMS | P | Czech | Ostrava | 1 | Compulsory | study plan | |||

2022/2023 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | VM | K | Czech | Ostrava | 1 | Compulsory | study plan | |||

2022/2023 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | VM | P | Czech | Ostrava | 1 | Compulsory | study plan | |||

2021/2022 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | NMS | P | Czech | Ostrava | 1 | Compulsory | study plan | |||

2021/2022 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | VM | K | Czech | Ostrava | 1 | Compulsory | study plan | |||

2021/2022 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | VM | P | Czech | Ostrava | 1 | Compulsory | study plan | |||

2021/2022 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | NMS | K | Czech | Ostrava | 1 | Compulsory | study plan | |||

2020/2021 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2020/2021 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2020/2021 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | NMS | K | Czech | Ostrava | 1 | Compulsory | study plan | |||

2020/2021 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | VM | P | Czech | Ostrava | 1 | Compulsory | study plan | |||

2020/2021 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | NMS | P | Czech | Ostrava | 1 | Compulsory | study plan | |||

2020/2021 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | VM | K | Czech | Ostrava | 1 | Compulsory | study plan | |||

2019/2020 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2019/2020 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2019/2020 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | NMS | P | Czech | Ostrava | 1 | Compulsory | study plan | |||

2019/2020 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | VM | P | Czech | Ostrava | 1 | Compulsory | study plan | |||

2019/2020 | (N0541A170007) Computational and Applied Mathematics | (S01) Applied Mathematics | NMS | K | Czech | Ostrava | 1 | Compulsory | study plan | |||

2019/2020 | (N0541A170007) Computational and Applied Mathematics | (S02) Computational Methods and HPC | VM | K | Czech | Ostrava | 1 | Compulsory | study plan | |||

2018/2019 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2018/2019 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2017/2018 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2017/2018 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2016/2017 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2016/2017 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2015/2016 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2015/2016 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 1 | Compulsory | study plan | ||||

2014/2015 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 1 | Choice-compulsory | study plan | ||||

2014/2015 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 1 | Choice-compulsory | study plan | ||||

2013/2014 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 1 | Choice-compulsory | study plan | ||||

2013/2014 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 1 | Choice-compulsory | study plan | ||||

2012/2013 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 1 | Choice-compulsory | study plan | ||||

2012/2013 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 1 | Choice-compulsory | study plan | ||||

2011/2012 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 1 | Choice-compulsory | study plan | ||||

2011/2012 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 1 | Choice-compulsory | study plan | ||||

2010/2011 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | P | Czech | Ostrava | 1 | Choice-compulsory | study plan | ||||

2010/2011 | (N2647) Information and Communication Technology | (1103T031) Computational Mathematics | K | Czech | Ostrava | 1 | Choice-compulsory | study plan |

Block name | Academic year | Form of study | Study language | Year | W | S | Type of block | Block owner |
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2023/2024 Summer |

2019/2020 Summer |

2017/2018 Summer |

2016/2017 Summer |

2015/2016 Summer |

2014/2015 Summer |

2012/2013 Summer |