| Course Unit Code | 470-4502/01 |
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| Number of ECTS Credits Allocated | 6 ECTS credits |
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| Type of Course Unit * | Compulsory |
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| Level of Course Unit * | Second Cycle |
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| Year of Study * | First Year |
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| Semester when the Course Unit is delivered | Summer 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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| 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. |
| Learning Outcomes of the Course Unit |
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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.
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| Course Contents |
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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. |
| Recommended or Required Reading |
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| Required Reading: |
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K. Rektorys:. Variational Methods in Mathematics, Science and Engineering, D. Reidel Publ. Comp, NY 1975
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K. Rektorys: Variační metody v inženýrských problémech a v problémech matematické fyziky, SNTL Praha 1974.
C. Johnson: Numerical solution of partial differential equations by the finite element method, Cambridge Univ. Press, 1995
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| Recommended Reading: |
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| C. Johnson: Numerical solution of partial differential equations by the finite element method, Cambridge Univ. Press, 1995 |
| C. Johnson: Numerical solution of partial differential equations by the finite element method, Cambridge Univ. Press, 1995 |
| Planned learning activities and teaching methods |
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| Lectures, Tutorials |
| 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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| Exercises evaluation and Examination | Credit and Examination | 100 (100) | 51 |
| Exercises evaluation | Credit | 30 | 15 |
| Examination | Examination | 70 | 21 |