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Computational and analytical a posteriori error estimates for finite element methods
Segeth, Karel
The analytical a posteriori error estimates are oriented to the use in h-methods, are usually constructed only for lowest-order polynomial approximation, and often depend on unknown constatns or functions. In this review paper, we present several error estimation procedures for some particular linear partial differential problems with special regards to the needs of the hp-method. We compare the advantages and drawbacks of a posteriori error estimators including computational ones.
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Approaches to parallel implementation of the BDDC method
Šístek, Jakub ; Burda, P. ; Čertíková, M. ; Novotný, J.
During past several years, we have implemented and tested various approaches to domain decomposition methods, especially the Balancing Domain Decomposition Method by Constraints (BDDC). The goal of this paper is to summarize our experience with parallel implementation of such algorithms and to suggest ways to an implementation of the BDDC method that would be efficient on very large number of cores of computers of near future.
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On selections of constraints for the BDDC method
Čertíková, M. ; Šístek, Jakub ; Novotný, J. ; Burda, P.
The Balancing Domain Decomposition by Constraints (BDDC) method is an iterative substructuring domain decomposition method which uses a coarse space. The choice of coarse constraints on continuity has strong influence on convergence of the method. The goal of this paper is to compare the performance of several algorithms for selection of the coarse constraints applied to both test and industrial 3D linear elasticity problems and confront results obtained for typical test problems with results for industrial problems.
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Fluid flow in cavity solved by finite element method
Burda, P. ; Novotný, J. ; Šístek, Jakub
The problem of singularities caused by boundary conditions is studied in the flow of lid driven cavity. The asymptotic behaviour near the singularity points is used together with the apriori error estimates of the finite element solution, in order to design the finite element mesh adjusted to singularity. A posteriori error estimates are used as the principal tool for error analysis. Thus we obtain very precise solution in the vicinity of the singularity. Numerical results are presented.
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Development of natural differentiation in mathematics classroom
Hošpesová, A. ; Tichá, Marie
The need that pupils achieve functional mathematical literacy grows. It makes considerable demands on teachers' professional competences, including their ability to react on heterogeneity and to create conditions for developmnet of all pupils' educational prerequisites. Heterogeneity is not grasped as a problem but as something natural and in some aspects challenging.
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Geometrical imagination as a part of mathematical literacy
Roubíček, Filip
The paper deals with geometrical imagination as ability to interpret geometrical content, evoke images and manipulate with them. It describes approaches to teaching of geometry at primary school (natural geometry, principles of didactical structure of geometry) and activities for development geometrical imagination of pupils.
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