No (215)
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215
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Fluid flow in cavity solved by finite element method
Burda, P.; Novotný, J.; Šístek, Jakub
2010 - English
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.
Keywords:
FEM; incompressible flow; cavity; singularities
Available on request at various institutes of the ASCR
Fluid flow in cavity solved by finite element method
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 ...
Natural Differentiation in Mathematics (NaDiMa)
Dolk, M.; Hošpesová, A.; Krauthausen, G.; Roubíček, Filip; Scherer, P.; Selle, A.; Swoboda, E.; Tichá, Marie
2009 - English
Coping with heterogeneity and motivation of all students independent from their capabilities, is one of the great challenges in primary school, especially for teaching and learning mathematics. In the project NaDiMa several substantial learning environments enabling "natural differentiation" were designed, tested in the classroom and will be analysed. Zvládnout různorodost žáků a motivovat je nezávisle na jejich schopnostech a předpokladech představuje velkou výzvu pro vyučování matematice. V rámci řešení projektu NaDiMa byla vytvořena a ve vyučování vyzkoušena různá podnětná prostřední umožňující přirozenou diferenciaci. Tato prostředí byla analyzována.
Keywords:
natural differentiation; motivation; substantial learning environment
Available at various institutes of the ASCR
Natural Differentiation in Mathematics (NaDiMa)
Coping with heterogeneity and motivation of all students independent from their capabilities, is one of the great challenges in primary school, especially for teaching and learning mathematics. In the ...
Lesson study - Could it work for you?
Doing, B.; Groves, S.; Macháčková, Jana
2009 - English
In Japan, lesson study occurs across many curriculum areas, mainly at the elementary school level, and to a lesser extent junior secondary. Lesson study has four phases: goal setting and planning, teaching the "research lesson - enabling the lesson observation; the post-lesson discussion; and the resulting consolidation of learning, which has many far-reaching consequences. It could be said that research lesson make participants and observers think quite profoundly about specific and general aspect of teaching. Na základních školách v Japonsku bývá v mnoha vyučovacích předmětech organizována "lesson study". Lesson study má čtyři fáze: stanovení a plánování cíle hodiny, "výzkumnou hodinu", vyučovací hodinu, ve které je umožněno pozorování výuky, diskuzi po hodině a následné sjednocení výuky s výhledem na dlouhodobou perspektivu. Je možné říct, že tyto hodiny nutí účastníky a pozorovatele přemýšlet poměrně hluboce o specifických i obecných aspektech vyučování.
Keywords:
lesson study - research lesson; elementary level; mathematics education
Available at various institutes of the ASCR
Lesson study - Could it work for you?
In Japan, lesson study occurs across many curriculum areas, mainly at the elementary school level, and to a lesser extent junior secondary. Lesson study has four phases: goal setting and planning, ...
On one geometrical environment supporting natural differentiation
Macháčková, Jana; Roubíček, Filip
2009 - English
The poster deals with development of geometry thinging at primary school level and motivation of pupils via natural differentiation. The learning environment that is based on describing and drawing a way in a plan is illustrated. Poster se zabývá rozvojem geometrického myšlení na prvním stupni základní školy motivací žáků prostřednictvím přirozené diferenciace. Ilustruje výukové prostředí založené na popisování a zakreslování cesty v plánu.
Keywords:
teaching of geometry; learning environment; motivation
Available at various institutes of the ASCR
On one geometrical environment supporting natural differentiation
The poster deals with development of geometry thinging at primary school level and motivation of pupils via natural differentiation. The learning environment that is based on describing and drawing a ...
Opportunities of development of language structures in mathematics
Roubíček, Filip
2009 - English
The paper deals with communication as an element of activities in mathematics classroom and differences between pupil's and teacher's mathematical language that cause educational obstacles. The use of a specific representational environment for language development in everyday teaching is illustrated. Článek pojednává o komunikaci jako součásti matematických aktivit a rozdílech mezi žákovým a učitelovým jazykem, které způsobují vzdělávací překážky. Ilustruje užití specifických reprezentačních prostředí pro rozvoj jazyka v běžném vyučování.
Keywords:
teaching of mathematics; communication; language
Available on request at various institutes of the ASCR
Opportunities of development of language structures in mathematics
The paper deals with communication as an element of activities in mathematics classroom and differences between pupil's and teacher's mathematical language that cause educational obstacles. The use of ...
Implementation of the BDDC method based on the frontal and multifrontal algorithm
Šístek, Jakub; Novotný, Jaroslav; Burda, Pavel; Čertíková, Marta
2009 - English
A parallel implementation of the BDDC method is presented. It is based on frontal solver for subdomain problems, while the coarse problem is solved by a multifrontal algorithm. Results for an industrial problem of mine reel are included. Je prezentována paralelní implementace metody BDDC, která je založena na frontálním řešiči pro subdoménové problémy. Hrubý problém je řešen multifrontálním algoritmem. Jsou zahrnuty výsledky pro průmyslový problém kola důlního výtahu.
Keywords:
BDDC; domain decomposition; iterative substructuring; linear elasticity
Available at various institutes of the ASCR
Implementation of the BDDC method based on the frontal and multifrontal algorithm
A parallel implementation of the BDDC method is presented. It is based on frontal solver for subdomain problems, while the coarse problem is solved by a multifrontal algorithm. Results for an ...
A posteriori error estimates for adaptive finite element methods
Segeth, Karel
2008 - English
While the classical a posteriori error estimates are oriented to the use in h-finite element methods the contemporary higher-order hp-methods usually require new approaches in a posteriori error estimation. We present examples of error estimation procedures for some model linear problems with a special regard to the needs of the hp-method. In the conclusion, we assess the advantages and drawbacks of a posteriori error estimates including computational error estimates (reference solutions). Zatímco klasické aposteriorní odhady chyby jsou zaměřeny na použití v h-metodě konečných prvků, soudobé hp-metody vyšších řádů vyžadují nový přístup při aposteriorním odhadování chyby. Uvádíme příklady procedur pro odhad chyby pro některé modelování lineárního problému se zvláštním zřetelem k potřebám hp-metody. Na závěr zvažujeme přednosti a nevýhody aposteriorních odhadů chyby včetně výpočetních odhadů ( inferenčních řešení).
Keywords:
hp-adaptive finite element method; a posteriori error estimators; computaional error estimates
Available at various institutes of the ASCR
A posteriori error estimates for adaptive finite element methods
While the classical a posteriori error estimates are oriented to the use in h-finite element methods the contemporary higher-order hp-methods usually require new approaches in a posteriori error ...
On efficiency of the criterion for equivalence of linear differential equations
Neuman, František
2008 - English
The study of the effectiveness of the criterion of equivalence of linear differential equations Studium efektivnosti kriteria ekvivalence lineárních diferenciálních rovnic
Keywords:
linear differential equations; equivalence; effectiveness
Available at various institutes of the ASCR
On efficiency of the criterion for equivalence of linear differential equations
The study of the effectiveness of the criterion of equivalence of linear differential equations
Studium efektivnosti kriteria ekvivalence lineárních diferenciálních rovnic
Space-time adaptive hp-FEM: Methodology overview
Šolín, P.; Segeth, Karel; Doležel, I.
2008 - English
We present a new class of self-adaptive higher-order finite element methods (hp-FEM) which are free of analytical error estimates and thus work equally well for virtually all PDE problems ranging from simple linear elliptic equations to complex time-dependent nonlinear multiphysics coupled problems. The methodology was used to solve various types of problems. In this paper we use a nonlinear combustion problem for illustration. Zavádíme novou třídu samoadaptivních metod konečných prvků vyšších řádů (hp-FEM), které neobsahují analytické odhady chyby a pracují tak stejně dobře pro všechny úlohy pro parciální diferenciální rovnice od jednoduchých lineárních eliptických rovnic po složité časově závislé nelineární fyzikální sdružené úlohy. Uvedená metodologie byla užita pro řešení různých typů úloh. V tomto příspěvku uvádíme pro ilustraci nelineární úlohu spalování.
Keywords:
higher-order finite element methods; error estimates; combustion problem
Available at various institutes of the ASCR
Space-time adaptive hp-FEM: Methodology overview
We present a new class of self-adaptive higher-order finite element methods (hp-FEM) which are free of analytical error estimates and thus work equally well for virtually all PDE problems ranging ...
Different forms of modelling as a support of communication between the teacher and the pupil
Roubíček, Filip
2007 - English
The poster includes some illustrations of representational environments investigated in the frame of mathematics classes at an elementary school, for example usage of various types of puzzles, geometry of folded sheet of paper and geometry using strings. Poster obsahuje několik ukázek reprezentačních prostředí zkoumaných v rámci výuky matematiky na základní škole, například užití různých skládaček, geometrie překládaného papíru a provázkové geometrie
Keywords:
teaching of geometry; geometrization; representational environment
Available on request at various institutes of the ASCR
Different forms of modelling as a support of communication between the teacher and the pupil
The poster includes some illustrations of representational environments investigated in the frame of mathematics classes at an elementary school, for example usage of various types of puzzles, ...
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