Course Details
Numerical methods for the variational problems
Academic Year 2024/25
DA66 course is part of 7 study plans
D-K-C-SI (N) / VHS Winter Semester 2nd year
D-K-C-SI (N) / MGS Winter Semester 2nd year
D-K-C-SI (N) / PST Winter Semester 2nd year
D-K-C-SI (N) / FMI Winter Semester 2nd year
D-K-C-SI (N) / KDS Winter Semester 2nd year
D-K-C-GK / GAK Winter Semester 2nd year
D-K-E-SI (N) / PST Winter Semester 2nd year
Course Guarantor
Institute
Language of instruction
Czech
Credits
10 credits
Semester
winter
Forms and criteria of assessment
examination
Offered to foreign students
Not to offer
Course on BUT site
Lecture
13 weeks, 3 hours/week, elective
Syllabus
1. Functional and its Euler equation, the simlest problem ov 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.