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Lecturer(s)
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Machalová Jitka, doc. RNDr. Ph.D., MBA
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Burkotová Jana, Mgr. Ph.D.
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Course content
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1. Fundamental concepts and propositions of variational calculus. Formulations of variational calculus problems. 2. Fundamental theorems of variational calculus. 3. Variational formulations and solvability of elliptic boundary value problems. 4. Elliptic boundary value problems of the 4nd order, bending of Euler-Bernoulli beam and a thin plate. 5. Elliptic variational inequalities. 6. Ritz method for variational problems. Principle of the method, convergence conditions and error estimation. Choice of basis functions. Examples. 7. Ritz and Galerkin method for variational equations. Principle of the method, convergence conditions and error estimation. 8. Definition of a finite element. P-unisolvency. Local basis functions. Typical examples for finite elements of Lagrange's and Hermite's type. Finite element spaces. 9. Introduction to convergence theory of the FEM. Cea's lemma. Bramble-Hilbert lemma. Reference elements. Analysis of order of convergence for linear triangular elements. 10. Finite element approximation of the solution to parabolic problems. Weak formulation of parabolic problems. Galerkin method for time dependent problems. Principle of the Rothe's method.
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Learning activities and teaching methods
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unspecified
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Learning outcomes
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Understand and be able to use the most widespread computational method for boundary value problems.
Knowledge Gain knowledge about well-known method for solution of boundary value problems.
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Prerequisites
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Standard knowledge from mathematical and functional analysis.
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Assessment methods and criteria
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unspecified
Credit: the student has to compute a given example. Exam: the student has to understand the subject and be acquainted with theoretical and practical methods.
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Recommended literature
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J. Machalová, H. Netuka. (2015). Metoda konečných prvků. Univerzita Palackého v Olomouci.
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J. Machalová, H. Netuka. (2014). Variační metody. Univerzita Palackého v Olomouci, Olomouc.
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J.N. Reddy. (2006). An Introduction to the Finite Element Method, Boston, Mass. McGraw-Hill.
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S.C. Brenner, L.R. Scott. (2008). The Mathematical Theory of Finite Element Methods. Springer.
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S.D. Rajan. (2021). Finite Element Analysis for Engineers.
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