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Mathematical foundations of the finite element method for the numerical solution of partial differential equations.
Last update: T_KNM (19.05.2008)
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The course gives students a knowledge of mathematical basics of the finite element method. Last update: T_KNM (16.05.2008)
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Brenner S.,Scott R.: The mathematical theory of finite element methods, 1994 Ciarlet, P.G.: The finite element method for elliptic problems, l978 Haslinger J.: Metoda konečných prvků, skripta MFF UK Thomée V.: Galerkin finite element methods for parabolic problems, 1997 Last update: T_KNM (16.05.2008)
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Lectures and tutorials in a lecture hall. Last update: T_KNM (16.05.2008)
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Examination according to the syllabus. Last update: T_KNM (16.05.2008)
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Short introduction to Sobolev spaces, basic ideas of the finite element method, abstract variational problem, Lax-Milgram lemma, triangulations of the computational domain. Examples of finite elements defined on simplices, rectangles and hexahedra. Affine equivalence of finite elements, concept of a reference finite element, general definition of finite element spaces. Interpolation in Sobolev spaces. Approximation properties of finite element spaces. Convergence of discrete solutions of elliptic problems. Numerical integration, First Strang's lemma, Bramble-Hilbert lemma. Error estimates for finite element discretizations of elliptic problems in the presence of numerical integration. Further variational crimes: nonconforming and isoparametric finite elements, approximation of the boundary. Finite element discretization of parabolic problems: error estimates for a semidiscretization in space and for the fully discretized problem. Last update: T_KNM (16.05.2008)
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Students are expected to have attended a basic course of functional analysis and to have attended or to attend a course on the modern theory of partial differential equations, e.g., NDIR045. Last update: T_KNM (16.05.2008)
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