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Lecturer(s)
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Kantor Martin, Ing. Ph.D.
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Course content
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1. Introduction to the mathematical apparatus used (vector, Hilbert, Banach space, standard matrix, function spaces, spaces Sobolevovy) 2. The basic principle of the finite element method - example of using the elliptical one-dimensional role, association and classical weak solution, error estimate 3. Variational method (Ritz and Galerkin formulation) 4. Weak formulation of two-dimensional boundary value problems - Dirichlet, Neumann boundary conditions 5. Construction of finite element space, the choice of bases, the triangulation, linear, quadratic and cubic elements, the equivalence of elements (the image on the reference triangle) 6. Application of finite element method for two-dimensional role - preparing the element stiffness matrix and global stiffness matrix, the core algorithm, the image on the reference triangle 7. Solution discrete tasks - the system of linear equations (direct, iterative, gradient methods) 8. Approximation theory finite element interpolation, a priori estimates of errors 9. Finite element method for elliptic, parabolic and hyperbolic problems, the convection-diffusion (Navier-Stokes equations)
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Learning activities and teaching methods
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unspecified
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Learning outcomes
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The course is aimed at introducing students to basic theory of finite element method (FEM) and its application in numerical methods for solving engineering problems.
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Prerequisites
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Basic knowledge of the theory and application the finite elements method.
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Assessment methods and criteria
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unspecified
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Recommended literature
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C. Johnson. Numerical Solution of Partial Differential Equations by the Finite Element Method. Cambridge University Press, 1992.
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E. Vitásek. Základy teorie numerických metod pro řešení diferenciálních rovnic. Academia, Praha, 1994.
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K. Rektorys. Variační metody. Academia, Praha, 1999.
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P. Sváček, M. Feistauer. Metoda konečných prvků. ČVUT Praha, 2006. ISBN ISBN 80-01-03522-.
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S.C. Brenner, L. R. Scott. The Mathematical Theory of Finite Element Methods. 2nd ed., Springer-Verlag, 2002.
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Thomas J. R. Hughes. The Finite Element Method: Linear Static and Dynamic Finite Element Analysis. Dover Publications, 2000.
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