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Numerical Methods II

Type of study Follow-up Master
Language of instruction Czech
Code 470-4502/01
Abbreviation NM2
Course title Numerical Methods II
Credits 6
Coordinating department Department of Applied Mathematics
Course coordinator doc. Ing. Dalibor Lukáš, Ph.D.

Subject syllabus

Lectures:
Mathematical formulations of boundary and initial value problems describing physical phenomena. Advantages of mathematical modeling and correct use of mathematical models.
Mathematical formulations of 2D and 3D problems.
Variational (weak) formulations. Energy functional and formulations. Existence and regularity of solutions.
Ritz-Galerkin method.
Finite element method in 1D.
Finite element method in 2D and 3D.
Programming of FEM.
Reference element. Isoparameteric finite elements.

FEM error. Apriori estimates.
Aposteriori estimates. Adaptive methods, optimal grids.
Nonconform and mixed methods. Nonlinear problems.


Tutorials:
Derivation of mathematical formulations of boundary and initial value problems for various physical phenomena.
Variational (weak) formulations.
Use of Ritz-Galerkin method.
FEM algorithm.
Programming, pre and postprocessing.

Solution to selected problems, discretization error.
Use of commercial software.



Projects:
Projects consist of a series of simple problems, the solution to which makes use of the theory. Projects may be concerned with programming of FEM.

Literature

K. Rektorys:. Variational Methods in Mathematics, Science and Engineering, D. Reidel Publ. Comp, NY 1975

Advised literature

C. Johnson: Numerical solution of partial differential equations by the finite element method, Cambridge Univ. Press, 1995