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Smooth approximation of data with applications to interpolating and smoothings
Segeth, Karel
In the paper, we are concerned with some computational aspects of smooth approximation of data. This approach to approximation employs a (possibly infinite) linear combinations of smooth functions with coefficients obtained as the solution of a variational problem, where constraints represent the conditions of interpolating or smoothing. Some 1D numerical examples are presented.
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Smooth approximation and its application to some 1D problems
Segeth, Karel
In the contribution, we are concerned with the exact interpolation of the data at nodes given and also with the smoothness of the interpolating curve and its derivatives. This task is called the problem of smooth approximation of data. The interpolating curve or surface is defined as the solution of a variational problem with constraints. We discuss the proper choice of basis systems for this way of approximation and present the results of several 1D numerical examples that show the quality of smooth approximation.
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Programs and Algorithms of Numerical Mathematics 15
Vejchodský, Tomáš ; Chleboun, J. ; Přikryl, Petr ; Segeth, Karel ; Šístek, Jakub
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.
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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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Programy a algoritmy numerické matematiky 14
Chleboun, Jan ; Přikryl, Petr ; Segeth, Karel ; Vejchodský, Tomáš
The book contains papers presented at the international seminar Programs and algorithms of numerical Mathematics 14 (PANM 14), held in Dolni Maxov, Czech Republic, June 1-6, 2008. It is the fourteenth 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.
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Aposteriorní odhady chyby pro adaptivní metody konečných prvků
Segeth, Karel
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).
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hp-metody konečných prvků adaptivní v prostoru i v čase: Přehled metodologie
Šolín, P. ; Segeth, Karel ; Doležel, I.
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.
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Programy a algoritmy numerické matematiky 13
Chleboun, Jan ; Segeth, Karel ; Vejchodský, Tomáš
The book contains papers presented at the international conference Programs and Algorithms of Numerical Mathematics 13(PANM 13) held in Prague, Czech Republic, May 28-31, 2006, in honor of Ivo Babuska´s 80th birthday. It is the thirteenth 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 algebra, etc.
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Porovnávání některých konečně prvkových aproximací hraničních vrstev
Segeth, Karel
The numerical solution of convection-diffusion problems with a dominant influence of convection plays important role in many scientific and engineering applications, such as viscous flow, fluid-structure interaction, transport models, and others. These problems typically exhibit, steep gradients, e.g. in the vicinity of solid walls, which are called boundary layers. Usually, piecewise-linear finite element methods combined with appropriate stabilization techniques are used to compute the solution. In this study we investigate the potential of the hp-FEM to facilitate the numerical treatment of this class of problems.
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