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