Course Details
Numerical methods for the variational problems
Academic Year 2024/25
DAB036 course is part of 23 study plans
DKA-E Winter Semester 2nd year
DKA-GK Winter Semester 2nd year
DKA-K Winter Semester 2nd year
DKA-M Winter Semester 2nd year
DKA-S Winter Semester 2nd year
DKA-V Winter Semester 2nd year
DPA-E Winter Semester 2nd year
DPA-GK Winter Semester 2nd year
DPA-K Winter Semester 2nd year
DPA-M Winter Semester 2nd year
DPA-S Winter Semester 2nd year
DPA-V Winter Semester 2nd year
DKC-E Winter Semester 2nd year
DKC-GK Winter Semester 2nd year
DKC-K Winter Semester 2nd year
DKC-M Winter Semester 2nd year
DKC-S Winter Semester 2nd year
DKC-V Winter Semester 2nd year
DPC-E Winter Semester 2nd year
DPC-GK Winter Semester 2nd year
DPC-K Winter Semester 2nd year
DPC-M Winter Semester 2nd year
DPC-S Winter Semester 2nd year
Course Guarantor
Institute
Language of instruction
Czech
Credits
10 credits
Semester
Forms and criteria of assessment
Offered to foreign students
Course on BUT site
Lecture
13 weeks, 3 hours/week, elective
Syllabus
- 1. Functional and its Euler equation, the simlest problem of calculus of variations.
- 2. Concrete examples of functionals and related Euler equations. Elementary solutions.
- 3. Derivation of an elliptic problem for ODE of degree 2, the problems of heat conduction and distribution of polution.
- 4. Discretization of the elliptic problem for ODE of degree 2 by the standard finite difference method, stability of numerical solutions.
- 5. Variational (weak) and minimization formulation of the elliptic problem for the elliptic problem for ODE of degree 2.
- 6. The Ritz and Galerkin methods.
- 7. Discretization of the elliptic problem for ODE of degree 2 by the finite element method.
- 8. Discretization of the variational formulation of the elliptic problem for ODE of degree 2 by the finite element method.
- 9. Discretization of the minimization formulation of the elliptic problem for ODE of degree 2 by the finite element method.
- 10. Discretization of the variational formulation of the elliptic problem for PDE of degree 2 by the finite element method.
- 11. Variational formulation and the finite element method for the linear elasticity problem.
- 12. Navier-Stokes equations and their numerical solution by the particle method.
- 13. A mathematical model of simultaneous distribution of moisture and heat in porous materials, discretizations.