Course Details

# Numerical methods for the variational problems

Academic Year 2023/24

DA66 course is part of 12 study plans

D-P-C-SI (N) / PST Winter Semester 2nd year

D-P-C-SI (N) / FMI Winter Semester 2nd year

D-P-C-SI (N) / KDS Winter Semester 2nd year

D-P-C-SI (N) / MGS Winter Semester 2nd year

D-P-C-SI (N) / VHS Winter Semester 2nd year

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

2. Differential problems: Classical and variational formulations of boundary-value differential problems. Discretization of stationary differential problems by the finite-difference, Galerkin Ritz methods. Standard time-discretizations of non-stationary differential problems.

3. Formulation and numerical solution of the heat-conduction problem, the linear elasticity problem, of the linear flow problems, of the Navier-Stokes equations and of selected models of simultaneous moisture and heat distribution in porous media.

Course Guarantor

Institute

Objective

Syllabus

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.

Prerequisites

Language of instruction

Czech

Credits

10 credits

Semester

Forms and criteria of assessment

Specification of controlled instruction, the form of instruction, and the form of compensation of the absences

Offered to foreign students

Course on BUT site

Lecture

13 weeks, 3 hours/week, elective

Syllabus