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On the quality of local flux reconstructions for guaranteed error bounds
Vejchodský, Tomáš
2015 - anglický
In this contribution we consider elliptic problems of a reaction-diffucion type discretized by the finite element method and study the quality of guaranteed upper bounds of the error. In particular, we concentrate on complementary error bounds whose values are determined by suitable flux reconstructions. We present numerical experiments comparing the performance of the local flux reconstruction of Ainsworth and Vejchodský [2] and the reconstruction of Braess and Schröberl [5]. We evaluate the efficiency of these flux reconstructions by their comparison with the optimal flux reconstruction computed as a global minimization problem.
Klíčová slova:
a posteriori error estimates; complementarity; index of effectivity; elliptic problem
Dokument je dostupný na externích webových stránkách.
On the quality of local flux reconstructions for guaranteed error bounds
In this contribution we consider elliptic problems of a reaction-diffucion type discretized by the finite element method and study the quality of guaranteed upper bounds of the error. In particular, ...
Talk about patterns in the mathematics classroom
Roubíček, Filip
2015 - anglický
The poster deals with the talk in the mathematics classroom which is focused on looking for relationships in a pattern. The communication of students is observed in the environment of geometrical patterns in a triangle grid and their transformation into arithmetic patterns or algebraic functions. It shows how pupils/students reason about relationships in these patterns and among these patterns, how they describe and express their generalizations in words or symbols.
Klíčová slova:
discourse; mathematics classroom; patterns
Plné texty jsou dostupné na vyžádání prostřednictvím repozitáře Akademie věd.
Talk about patterns in the mathematics classroom
The poster deals with the talk in the mathematics classroom which is focused on looking for relationships in a pattern. The communication of students is observed in the environment of geometrical ...
How primary school teachers posed problems for inquiry based mathematics education
Hošpesová, A.; Samková, L.; Tichá, Marie; Roubíček, Filip
2015 - anglický
The paper reports on a survey whose aim is to contribute to the research in the area of inquiry based mathematics education (IBME), primary school teacher training, and problem posing. The core of the study is an empirical survey with a qualitative design. We let pre-service and in-service primary school teachers pose problems which they believe enable IBME, perform the problems with pupils, and write self-reflections on this activity. We investigated the nature of the posed problems in relation to the self-reflections.
Klíčová slova:
inquiry based mathematics education; posing problems; primary school teacher training; pre-service and in-service teachers
Plné texty jsou dostupné na jednotlivých ústavech Akademie věd ČR.
How primary school teachers posed problems for inquiry based mathematics education
The paper reports on a survey whose aim is to contribute to the research in the area of inquiry based mathematics education (IBME), primary school teacher training, and problem posing. The core of the ...
A parallel finite element solver for unsteady incompressible Navier-Stokes equations
Šístek, Jakub
2015 - anglický
A parallel solver for unsteady incompressible Navier-Stokes equations is presented. It is based on the finite element method combined with the pressure-correction approach. Semi-implicit treatment of the convective term is considered, leading to five systems of linear algebraic equations to be solved in each time step. Krylov subspace iterative methods are employed for the solution of these systems with a particular emphasis on efficient parallel preconditioners. A simulation of a benchmark problem of incompressible viscous flow around a sphere at Reynolds number 300 is presented and compared with literature.
Klíčová slova:
pressure-correction; parallel algorithms; flow around a sphere
Dokument je dostupný na externích webových stránkách.
A parallel finite element solver for unsteady incompressible Navier-Stokes equations
A parallel solver for unsteady incompressible Navier-Stokes equations is presented. It is based on the finite element method combined with the pressure-correction approach. Semi-implicit treatment of ...
An application of the BDDC method to the Navier-Stokes equations in 3-D cavity
Hanek, M.; Šístek, Jakub; Burda, P.
2015 - anglický
We deal with numerical simulation of incompressible flow governed by the Navier-Stokes equations. The problem is discretised using the finite element method, and the arising system of nonlinear equations is solved by Picard iteration. We explore the applicability of the Balancing Domain Decomposition by Constraints (BDDC) method to nonsymmetric problems arising from such linearisation. One step of BDDC is applied as the preconditioner for the stabilized variant of the biconjugate gradient (BiCGstab) method. We present results for a 3-D cavity problem computed on 32 cores of a parallel supercomputer.
Klíčová slova:
incompressible fluid; Navier-Stoken equations; BDDC; Taylor-Hood finite element
Plné texty jsou dostupné v digitálním repozitáři Akademie Věd.
An application of the BDDC method to the Navier-Stokes equations in 3-D cavity
We deal with numerical simulation of incompressible flow governed by the Navier-Stokes equations. The problem is discretised using the finite element method, and the arising system of nonlinear ...
A note on tension spline
Segeth, Karel
2015 - anglický
Spline theory is mainly grounded on two approaches: the algebraic one (where splines are understood as piecewise smooth functions) and the variational one (where splines are obtained via minimization of quadratic functionals with constraints). We show that the general variational approach called smooth interpolation introduced by Talmi and Gilat covers not only the cubic spline but also the well known tension spline (called also spline in tension or spline with tension). We present the results of a 1D numerical example that show the advantages and drawbacks of the tension spline.
Klíčová slova:
smooth interpolation; tension spline; Fourier transform
Plné texty jsou dostupné v digitálním repozitáři Akademie Věd.
A note on tension spline
Spline theory is mainly grounded on two approaches: the algebraic one (where splines are understood as piecewise smooth functions) and the variational one (where splines are obtained via minimization ...
Preliminary results on Type I and II Kaluza–Klein reductions of vacuum spacetimes
Tintěra, Tomáš
2014 - anglický
We review the formalism used for the algebraic classification of higher- dimensional spacetimes, together with a few basic results in this field. Then we use this formalism to discuss some problems involving type I and II Kaluza–Klein reductions of vacuum spacetimes and to present a few results.
Klíčová slova:
algebraic classification; high-dimensional spacetime; vacuum
Plné texty jsou dostupné na vyžádání prostřednictvím repozitáře Akademie věd.
Preliminary results on Type I and II Kaluza–Klein reductions of vacuum spacetimes
We review the formalism used for the algebraic classification of higher- dimensional spacetimes, together with a few basic results in this field. Then we use this formalism to discuss some problems ...
Variability of Turing patterns in reaction-diffusion systems
Rybář, Vojtěch; Vejchodský, Tomáš
2014 - anglický
The paper presents a result about the number of distinct stationary solutions of a reaction-diffusion system exhibing the Turing instability. Relative frequency of observed solutions as they evolve from random initial conditions is analysed as well.
Klíčová slova:
diffusion driven instability; uniqueness; number of solutions
Dokument je dostupný na externích webových stránkách.
Variability of Turing patterns in reaction-diffusion systems
The paper presents a result about the number of distinct stationary solutions of a reaction-diffusion system exhibing the Turing instability. Relative frequency of observed solutions as they evolve ...
On simplicial red refinement in three and higher dimensions
Korotov, S.; Křížek, Michal
2013 - anglický
We show that in dimensions higher than two, the popular “red refinement” tech- nique, commonly used for simplicial mesh refinements and adaptivity in the finite element analysis and practice, never yields subsimplices which are all acute even for an acute father element as opposed to the two-dimensional case. In the three-dimensional case we prove that there exists only one tetrahedron that can be partitioned by red refinement into eight congruent subtetrahedra that are all similar to the original one.
Klíčová slova:
red refinement; finite element analysis
Dokument je dostupný na externích webových stránkách.
On simplicial red refinement in three and higher dimensions
We show that in dimensions higher than two, the popular “red refinement” tech- nique, commonly used for simplicial mesh refinements and adaptivity in the finite element analysis and practice, never ...
Posing problems with a given structure by pre-service teachers
Hošpesová, A.; Tichá, Marie
2013 - anglický
Posing problems of given structure is considered as a way of fostering teachers’ competence. We work with schemas from two perspectives: (a) schema as visualization of process of problem solving, (b) schema as representation of the structure of problem. We focused on the question: What problems do students pose if they are given a branched chain which represents the structure problem or solving procedure? Findings of ongoing research from work with teacher students are given.
Klíčová slova:
teachers' knowledge; scheme; structure of problem
Plné texty jsou dostupné na jednotlivých ústavech Akademie věd ČR.
Posing problems with a given structure by pre-service teachers
Posing problems of given structure is considered as a way of fostering teachers’ competence. We work with schemas from two perspectives: (a) schema as visualization of process of problem solving, (b) ...
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