A comparison of some a posteriori error estimates for fourth order problems
Segeth, Karel
2010 - English
In this survey contribution, we present and compare, from the viewpoint of adaptive computation, several recently published error estimation procedures for the numerical solution of biharmonic and some further fourth order problems including computational error estimates.
Keywords:
a posteriori error estimate; finite element method; fourth order problem
Available in digital repository of the ASCR
A comparison of some a posteriori error estimates for fourth order problems
In this survey contribution, we present and compare, from the viewpoint of adaptive computation, several recently published error estimation procedures for the numerical solution of biharmonic and ...
Programs and Algorithms of Numerical Mathematics 15
Vejchodský, Tomáš; Chleboun, J.; Přikryl, Petr; Segeth, Karel; Šístek, Jakub
2010 - English
The book contains papers presented at the international seminar Programs and algorithms of numerical Mathematics 15 (PANM 15), held in Dolni Maxov, Czech Republic, June 6-11, 2010. It is the fifteen volume in the series of the PANM proceedings. The topics of contributions include numerical methods for fluid flow modelling, the finite element method, a posteriori error estimates, topics from numerical linear atgebra, etc.
Keywords:
algorithms; numerical mathematics
Available in digital repository of the ASCR
Programs and Algorithms of Numerical Mathematics 15
The book contains papers presented at the international seminar Programs and algorithms of numerical Mathematics 15 (PANM 15), held in Dolni Maxov, Czech Republic, June 6-11, 2010. It is the fifteen ...
Approaches to parallel implementation of the BDDC method
Šístek, Jakub; Burda, P.; Čertíková, M.; Novotný, J.
2010 - English
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.
Keywords:
BDDC; domain decomposition; iterative substructuring; parallel computing
Available on request at various institutes of the ASCR
Approaches to parallel implementation of the BDDC method
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 ...
Tvoření úloh jako cesta k matematické gramotnosti
Tichá, Marie; Hošpesová, A.
2010 - Czech
V naší práci hledáme cesty efektivního rozvíjení matematické gramotnosti žáků a studentů. Usilujeme o to, aby žáci a studenti byli schopni používat matematiku jako vhodný nástroj při hledání cest, jak porozumět světu. Aby byli schopni porozumět matematickému textu, vybavovat si při tom potřebné pojmy a postupy. Jde nám o to, aby uměli své znalosti rozvíjet. Důraz klademe nejen na řešení rozmanitých úloh, do centra našich úvah o matematickém vzdělávání se dostává tvoření úloh. Jsme přesvědčeni, že tvoření úloh by mělo být jedním z centrálních témat vyučování matematice. Na tvoření úloh se můžemem dívat jako na cíl i prostředek matematického vzdělávání a dokonce také jako na diagnostický a motivační prostředek. In our work we search for ways of development of students' mathematical literacy. We aim at students' ability to utilize mathematics as a suitable tool for understanding of the world. Our aim is that students will be able to develop their knowledge. We stress not only solving of various problems. Also problem posing gets in the centre of our considerations on mathematical education. We believe that problem posing should be one of central topics of teaching of mathematics. It could be understand as aim as well as means of education and in addition also as diagnostic and motivating tool.
Keywords:
mathematical literacy; mathematical education; problem posing; problem solving
Available on request at various institutes of the ASCR
Tvoření úloh jako cesta k matematické gramotnosti
V naší práci hledáme cesty efektivního rozvíjení matematické gramotnosti žáků a studentů. Usilujeme o to, aby žáci a studenti byli schopni používat matematiku jako vhodný nástroj při hledání cest, jak ...
Rozvíjení přirozené diferenciace ve vyučování matematice
Hošpesová, A.; Tichá, Marie
2010 - Czech
Požadavky na úroveň funkční matematické gramotnosti rostou. To klade velké nároky na profesionální kompetence učitelů. K nim patří také dovednost reagovat na heterogenitu a vytvářet podmínky pro rozvoj vzdělávacích předpokladů všech žáků. Heterogenita není chápána jako problém, ale jako jev přirozený a v určitých oblastech podnětný. 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.
Keywords:
professional competences; heterogeneity; natural differentiation; substantial learning
Available at various institutes of the ASCR
Rozvíjení přirozené diferenciace ve vyučování matematice
Požadavky na úroveň funkční matematické gramotnosti rostou. To klade velké nároky na profesionální kompetence učitelů. K nim patří také dovednost reagovat na heterogenitu a vytvářet podmínky pro ...
A survey of global investigations of linear differential equations
Neuman, František
2010 - English
In contrast to the local investigations of behavior of solutions of linear differential equations, that started already in the XVII-th century, here we present a survey of methods and results of a global nature. It was possible to establish the unified theory of global properties of solutions of linear differential equations: to describe global canonical forms, distribution of zeros of solutions and other global properties of the equations studied.
Keywords:
linear differential equations; global canonical forms
Available at various institutes of the ASCR
A survey of global investigations of linear differential equations
In contrast to the local investigations of behavior of solutions of linear differential equations, that started already in the XVII-th century, here we present a survey of methods and results of a ...
Problem Posing, a Way to Teachers' Change
Hošpesová, A.; Tichá, Marie
2010 - English
Problem posing is an important component of a teacher's everyday activity. This contribution wants to show how problem posing may be used as a way to an increase in teachers' professionalism, to improvement of their subject didactic competence and also as a diagnostic and motivational tool.
Keywords:
professional competence of a teacher; teacher education; problem posing
Available on request at various institutes of the ASCR
Problem Posing, a Way to Teachers' Change
Problem posing is an important component of a teacher's everyday activity. This contribution wants to show how problem posing may be used as a way to an increase in teachers' professionalism, to ...
Some remarks on averaging in the BDDC method
Čertíková, M.; Burda, P.; Novotný, J.; Šístek, Jakub
2010 - English
In this paper, we introduce a general framework for derivation of the averaging operator, from hich the standard choices are recovered by simplifications. Then, an alternative approach derived by another simplification is proposed and tested on a 2D example.
Keywords:
BDDC method
Available in digital repository of the ASCR
Some remarks on averaging in the BDDC method
In this paper, we introduce a general framework for derivation of the averaging operator, from hich the standard choices are recovered by simplifications. Then, an alternative approach derived by ...
Integration in higher-order finite element method in 3D
Kůs, Pavel
2010 - English
Integration of higher-order basis functions is an important issue, that is not as straightforward as it may seem. In traditional low-order FEM codes, the bulk of computational time is a solution of resulting system of linear equations. In the case of higher-order elements the situation is different. Especially in three dimensions the time of integration may represent significant part of the computation.
Keywords:
finite element method
Available in digital repository of the ASCR
Integration in higher-order finite element method in 3D
Integration of higher-order basis functions is an important issue, that is not as straightforward as it may seem. In traditional low-order FEM codes, the bulk of computational time is a solution of ...
Study of using corners for BDDC in 3D
Čertíková, M.; Burda, P.; Novotný, J.; Šístek, Jakub
2010 - English
Existing algorithms for selection of corners in BDDC are atudied and a new algorithm is proposed. This combines advantages of previous algorithms. The new algorithm is applied to a benchmark and an industrial problem of linear elasticity.
Keywords:
BDDC; domain decomposition; iterative substructuring; linear elasticity
Available at various institutes of the ASCR
Study of using corners for BDDC in 3D
Existing algorithms for selection of corners in BDDC are atudied and a new algorithm is proposed. This combines advantages of previous algorithms. The new algorithm is applied to a benchmark and an ...
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