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Singularities in Electro- and Magnetostatics, and Their Efficient Resolution by hp-FEM
Segeth, Karel; Šolín, P.; Zítka, M.
2005 - English
In this paper we review the derivation of the partial differential equations describing electro- and magnetostatics, and give an overview of basic ideas of the hp-FEM. An example electrostatics problem is used to illustrate the superiority of the hp-FEM over the standard FEM. V článku jsou stručně odvozeny parciální diferenciální rovnice, které popisují elektro- a magnetostatiku a je uveden přehled základních myšlenek hp-metody kovových prvků. Pro ilustraci výhodnosti metod hp-FEM oproti standardní metodě FEM je užit modelový elektrostatický problém.
Keywords:
electrostatics; magnetostatics; potential equation
Available at various institutes of the ASCR
Singularities in Electro- and Magnetostatics, and Their Efficient Resolution by hp-FEM
In this paper we review the derivation of the partial differential equations describing electro- and magnetostatics, and give an overview of basic ideas of the hp-FEM. An example electrostatics ...
Some remarks on the asymptotic properties of the steady fall of a body in viscous fluids
Nečasová, Šárka
2004 - English
The article deals with the motion of a rigid body through a liqvid. We consider Stokes, Oseen and Navier-Stokes fluid. We investigate the exterior domain in3D case. The rotational motion is included in the consideration. Článek se zabývá pohybem rotujícího tělesa v tekutině. Uvažujeme Stokesův, Oseenův problém a Navier-Stokesovy rovnice. Je vyšetřován problém ve vnější oblasti, 3D. Uvažujeme i rotační pohyb.
Keywords:
steady fall of a body; Stokes problem; Oseen problem
Available at various institutes of the ASCR
Some remarks on the asymptotic properties of the steady fall of a body in viscous fluids
The article deals with the motion of a rigid body through a liqvid. We consider Stokes, Oseen and Navier-Stokes fluid. We investigate the exterior domain in3D case. The rotational motion is included ...
Higher-order methods of lines and error estimates for 2D nonlinear parabolic problems
Segeth, Karel; Šolín, P.; Zítka, M.
2004 - English
Numerical solution of initial-value problems for nonlinear parabolic equations by the finite element method becomes an essential tool for the development of new technologies in applications to electromagnetics, diffusion and heat transfer processes, chemistry, coupled problems, and others. The paper is concerned with the application of higher-order adaptive schemes. Numerické řešení počátečních úloh pro nelineární parabolické rovnice metodou konečnách prvků se stává zásadním prostředkem pro rozvoj nových technologií při aplikacích v elektromagnetice, difuzi a přenosu tepla, chemii, sdružených úloh a dalších problémů. Článek se zabývá aplikací adaptivních schémat vyššího řádu.
Keywords:
method of lines; nonlinear parabolic equations in 2D; finite element method
Available at various institutes of the ASCR
Higher-order methods of lines and error estimates for 2D nonlinear parabolic problems
Numerical solution of initial-value problems for nonlinear parabolic equations by the finite element method becomes an essential tool for the development of new technologies in applications to ...
Three ways of interpolation on finite elements
Šolín, Pavel; Segeth, Karel
2004 - English
Interpolation on finite elements usually occurs in a Hilbert space setting, which means that interpolation techniques involving orthogonal projection are an alternative for the traditional Lagrange nodal interpolation schemes. In addition to the Lagrange interpolation, this paper discusses the global orthogonal projection and the projection-based interpolation. These techniques are compared from the point of view of quality, efficiency, sensitivity to input parameters and other aspects. Interpolace na konečných prvcích se většinou formuluje v Hilbertově prostoru, což znamená, že interpolační techniky založené na ortogonální projekci jsou alternativou pro tradiční Lagrangeova uzlové interpolační techniky. Navíc se zvažuje globální ortogonální projekce a interpolace založené na projekci. Tyto techniky jsou porovnány z hlediska kvality, efektivnosti, citlivosti na vstupní parametry atd.
Keywords:
finite element method; language interpolation; orthogonal projection
Available at various institutes of the ASCR
Three ways of interpolation on finite elements
Interpolation on finite elements usually occurs in a Hilbert space setting, which means that interpolation techniques involving orthogonal projection are an alternative for the traditional Lagrange ...
Fast and Guaranteed a Posteriori Error Estimator
Vejchodský, Tomáš
2004 - English
The equilibrated residual method and the method of hypercircle are popular methods for a posteriori error estimation for linear elliptic problems. Both these methods are intended to produce guaranteed upper bounds of the energy norm of the error, but the equilibrated residual method is guaranteed only theoretically. The disadvantage of the hypercircle method is its globality, hence slowness. The combination of these two methods leads to local, hence fast, and guaranteed a posteriori error estimator. Populárními metodami pro aposteriorní odhady chyby v lineárních eliptických úlohách jsou metoda vyvýžených residuí a metoda hyperkruhu. Obě tyto metody mají dávat zaručenou horní mez energetické normy chyby, ovšem metoda vyvážených residuí je zaručená pouze teoreticky. Nevýhodou metody hyperkruhu je její globálnost a tedy pomalost. Kombinace obou metod vede na lokální, tedy rychlý a zaručený aposteriorní odhad chyby.
Keywords:
elliptic problem; a posteriori error estimator; equilibrated residual method
Available at various institutes of the ASCR
Fast and Guaranteed a Posteriori Error Estimator
The equilibrated residual method and the method of hypercircle are popular methods for a posteriori error estimation for linear elliptic problems. Both these methods are intended to produce guaranteed ...
Programs and algorithms of numerical mathematics 12
2004 - English
This book contains more than 30 papers presented at the seminar Programs and Algorithms of Numerical Mathematics held in Dolní Maxov, Czech Republic, June 6-11, 2004. The contributions deal mostly with the finite element method and its applications. Other subjects, as spline construction, numerical linear algebra algorithms, or optimization, for example, are also covered. Sborník obsahuje více než 30 příspěvků přednesených na semináři Programy a algoritmy numerické matematiky konaném v Dolním Maxově 6.-11. června 2004. Většina příspěvků se zabývá metodou konečných prvků a jejími aplikacemi. Jsou však zastoupena i další témata, např. konstrukce spline funkcí, algoritmy numerické lineární algebry nebo optimalizace.
Keywords:
finite element method; discontinous Galerkin method; flow
Available at various institutes of the ASCR
Programs and algorithms of numerical mathematics 12
This book contains more than 30 papers presented at the seminar Programs and Algorithms of Numerical Mathematics held in Dolní Maxov, Czech Republic, June 6-11, 2004. The contributions deal mostly ...
On cumulative 13C breath tests: An effort to improve the accuracy of test results revealed a substantial uncertainty in input data
Chleboun, Jan; Kocna, P.
2004 - English
In cumulative 13C breath tests, the estimation of CO2 production rate is a key issue. Two different estimates are compared. It is investigated why these estimates deliver rather different values. Pro kumulativní dechové testy s uhlíkem 13C je podstatný odhad produkce CO2. Jsou srovnávány dvě různé metody odhadu. Zkoumá se, proč tyto metody poskytují značně rozdílné hodnoty odhadu.
Keywords:
13C breath test; CO2 production rate; uncertainty
Available at various institutes of the ASCR
On cumulative 13C breath tests: An effort to improve the accuracy of test results revealed a substantial uncertainty in input data
In cumulative 13C breath tests, the estimation of CO2 production rate is a key issue. Two different estimates are compared. It is investigated why these estimates deliver rather different ...
Selfreflection and improving mathematics classroom culture
Hošpesová, A.; Tichá, Marie
2004 - English
Cultivation of teachersďself-reflection and systematic conduction of collective reflection can change character and promote quality of personaly oriented education. Therefore we aim at creation of supporting conditions for realizing these activies. In this contribution we show how a choosen group of primary shool teachers perceived and evaluated their competencies in the course. Kultivace sebereflexe učitelů a soustavné provádění kolektivní reflexe může měnit charakter a zkvalitńovat osobnostně orientované vzdělávání. Proto se snažíme o vytváření podmínek, které podporují realizaci těchto aktivit. V tomto příspěvku ukazujeme, jak skupina učitelů-elementaristů chápe a hodnotí své kompetence v procesu.
Keywords:
self-reflection; collective reflection; person-centered education
Available at various institutes of the ASCR
Selfreflection and improving mathematics classroom culture
Cultivation of teachersďself-reflection and systematic conduction of collective reflection can change character and promote quality of personaly oriented education. Therefore we aim at creation of ...
Semiotic Approach as a Methodological Basis in the Didactics of Mathematics
Roubíček, Filip
2003 - English
The paper deals with the parallel between the semiotic concept "sign" and the didactic concept "representation" and the semiotic analysis of pupilďs communication in lessons of geometry. Článek se zabývá paralelou mezi sémiotickým pojmem "znak" a didaktickým pojmem "reprezentace" a sémiotickou analýzou žákovské komunikace ve vyučování geometrii.
Keywords:
mathematics education; semiotics; representation
Available at various institutes of the ASCR
Semiotic Approach as a Methodological Basis in the Didactics of Mathematics
The paper deals with the parallel between the semiotic concept "sign" and the didactic concept "representation" and the semiotic analysis of pupilďs communication in lessons of geometry....
Dirichlet problem for the Laplace equation in a cracked domain with jump conditions on cracks
Medková, Dagmar
2003 - English
The Dirichlet problem for the Laplace equation in a cracked domain with jump conditions on cracks is studied. The uniqueness and the existence of a solution is shown and the solution is calculated.
Keywords:
Laplace equation; crack; boundary value problem
Available at various institutes of the ASCR
Dirichlet problem for the Laplace equation in a cracked domain with jump conditions on cracks
The Dirichlet problem for the Laplace equation in a cracked domain with jump conditions on cracks is studied. The uniqueness and the existence of a solution is shown and the solution is calculated.
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