Course Details

# Numerical methods for the variational problems

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

summer

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.