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Recent Submissions

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    Vzpomínkové odpoledne a seminář Metoda konečných prvků dnes ke 100. výročí narození profesora Miloše Zlámala: kompletní sborník
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, 2025-11-01) Franců, Jan
    Kompletní sborník ze Vzpomínkového odpoledne a semináře Metoda konečných prvků dnes ke 100. výročí narození profesora Miloše Zlámala
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    Adaptive mesh refinement and a posteriori error estimates
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, 2025-11-01) Vejchodský, Tomáš
    This short contribution is intended mainly for mathematicians who are not specialists in numerical analysis but would like to understand better the fundamental features of the finite element method. First, we review the finite element method for linear elliptic partial differential equations of second order. Then we concentrate on the main ideas of a priori and a posteriori error estimates, convergence and adaptive mesh refinement. We especially emphasize the pioneering convergence result of Professor Miloš Zlámal and present some modern results from the theory of the finite element method. We use several numerical examples to illustrate the presented results.
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    Item type:Item, Access status: Open Access ,
    V zemi klokanů
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, 2025-11-01) Aujeský, Antonín
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    Item type:Item, Access status: Open Access ,
    Professor Miloš Zlámal – his life and work
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, 2025-11-01) Křížek, Michal
    A brief biography of Professor Miloš Zlámal is presented. Then we focus on the mathematical problems he dealt with. In the first period there were various properties of analytical solutions of ordinary and partial differential equations. His main results are in the theory of the finite element method as the minimum angle condition guaranteeing convergence, curved finite elements, superconvergence, the so-called mortar finite elements and semiconductor equations.
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    Item type:Item, Access status: Open Access ,
    Finite element hp-methods for partial differential equations
    (Vysoké učení technické v Brně, Fakulta strojního inženýrství, 2025-11-01) Dolejší, Vít
    We deal with the numerical solution of partial differential equations using finite element method whose mathematical background was built in 60's by prof. Zlámal. We focus on the hp-mesh adaptive methods that combine the refinement of mesh elements and the variation of the degree of polynomial approximation. The hp-method can give the exponential rate of convergence of the error with respect to the number of degrees of freedom. We present several theoretical results, which are supported by numerical experiments.