Finite Elements method

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Department of Mathematics

Synopsis:

Hilbert's spaces

Bilinear forms and functionals

Quadratic functional, symmetry, positive definitness, theorem about the minimum and relation to the equation

Riesz's theorem and Lax-Milgram's theorem

Finite element method, convergence (generally for nonsymmetric operator) - Rieszs and Galerkins method

It can converge slowly

Better regularity converges better

The least square method

Variational crimes

Selection of base functions: h-version, p-version, hp-version, hierarchical base, cascade

Linear system preparation

Methods of solution of the resulting systems

- direct procedures

- iterative procedures

- possibilities of preconditioning

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The course is a part of the following study plans: