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The aim of this course is to present the mathematical theory of finite element methods and
their applications in solving linear elliptic equations. This covers: approximation theory for
mappings preserving polynomials , application to the Lagrange and Hermite interpolation of
functions in multidimensional space , description of the most frequently used finite elements, the error analysis,
numerical integration in FEM.
Last update: T_KNM (28.04.2015)
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Credit is not required for the exam.
Credit will be given for successful solutions of at least 50 % homeworks which will be given to the students regularly during the semester. The solutions of the homeworks have to be submitted via SIS till the deadlines. If a student will not acquire the credit for solutions of homeworks, the credit can be obtained for a successful written test (at least 50% points). The credit test can be repeated twice. Last update: Knobloch Petr, prof. Mgr., Dr., DSc. (10.10.2020)
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V. Dolejší, P. Knobloch, V. Kučera, M. Vlasák: Finite element methods: Theory, applications and implementations, Matfyzpress, Praha, 2013 J. Haslinger: Metoda konečných prvků pro řešení variačních rovnic a nerovnic eliptického typu, skripta, Praha 1980 P.G. Ciarlet: The Finite Element Method for Elliptic Problems, Studies in Mathematics and its Applications 4, North Holland Publishing Company, Amsterdam, 1978 S.C. Brenner, L.R.Scott: The Mathematical Theory of Finite Element Methods, Text in Applied Mathematics 15, Springer-Verlag, 2008 A. Ern, J.-L. Guermond: Theory and Practice of Finite Elements, Springer-Verlag, New York, 2004 Last update: Knobloch Petr, prof. Mgr., Dr., DSc. (11.10.2017)
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The exam is oral.
The requirements for the exam correspond to the syllabus of the subject in the extent that was presented at the lecture. Last update: Kučera Václav, doc. RNDr., Ph.D. (29.10.2019)
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abstract variational problem, Lax-Milgram lemma; Galerkin approximation, Cea's lemma; Lagrange and Hermite finite elements, concept of affine equivalence; construction of finite element spaces, satisfaction of stable boundary conditions; approximation theory in Sobolev spaces, application to Lagrange and Hermite interpolation of functions; error estimates for Galerkin approximations in the energy and L2 norm; numerical integration in FEM, errors of quadrature formulas; error of finite element approximation in the presence of numerical integration; FEM for parabolic problems
Last update: Knobloch Petr, prof. Mgr., Dr., DSc. (07.09.2020)
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Classical theory of partial differential equations of the 2nd order, basics of functional analysis. Last update: Haslinger Jaroslav, prof. RNDr., DrSc. (12.05.2019)
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