scholarly journals On a discrete norm for polynomials

2012 ◽  
Vol 396 (2) ◽  
pp. 425-433 ◽  
Author(s):  
R. Fournier ◽  
S. Ruscheweyh ◽  
L. Salinas C.
Keyword(s):  
Discrete Norm

scholarly journals Explicit Finite Difference Methods for the Delay Pseudoparabolic Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
I. Amirali ◽  
G. M. Amiraliyev ◽  
M. Cakir ◽  
E. Cimen
Keyword(s):  
Finite Difference ◽  
Finite Difference Methods ◽  
Time Integration ◽  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Energy Estimates ◽  
Fully Discrete ◽  
Discrete Norm ◽  
Explicit Finite Difference ◽  
Initial Boundary Value

Finite difference technique is applied to numerical solution of the initial-boundary value problem for the semilinear delay Sobolev or pseudoparabolic equation. By the method of integral identities two-level difference scheme is constructed. For the time integration the implicit rule is being used. Based on the method of energy estimates the fully discrete scheme is shown to be absolutely stable and convergent of order two in space and of order one in time. The error estimates are obtained in the discrete norm. Some numerical results confirming the expected behavior of the method are shown.

scholarly journals Generalized weighted Besov spaces on the Bessel hypergroup

2006 ◽  
Vol 4 (1) ◽  
pp. 91-111
Author(s):  
Miloud Assal ◽  
Hacen Ben Abdallah
Keyword(s):  
Besov Spaces ◽  
Generalized Convolution ◽  
Smooth Functions ◽  
General Properties ◽  
Generalized Translation ◽  
Discrete Norm ◽  
Type Spaces ◽  
Translation Operators ◽  
Weighted Besov Spaces ◽  
Besov Type Spaces

In this paper we study generalized weighted Besov type spaces on the Bessel-Kingman hypergroup. We give different characterizations of these spaces in terms of generalized convolution with a kind of smooth functions and by means of generalized translation operators. Also a discrete norm is given to obtain more general properties on these spaces.

scholarly journals Comparative Study on Numerical Methods for Singularly Perturbed Advanced-Delay Differential Equations

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
P. Hammachukiattikul ◽  
E. Sekar ◽  
A. Tamilselvan ◽  
R. Vadivel ◽  
N. Gunasekaran ◽  
...  
Keyword(s):  
Differential Equations ◽  
Delay Differential Equations ◽  
Shishkin Mesh ◽  
Singularly Perturbed ◽  
Diffusion Type ◽  
Convection Diffusion ◽  
Discrete Norm ◽  
Difference Methods ◽  
Second Order Convergence ◽  
Delay Differential

In this paper, we consider a class of singularly perturbed advanced-delay differential equations of convection-diffusion type. We use finite and hybrid difference schemes to solve the problem on piecewise Shishkin mesh. We have established almost first- and second-order convergence with respect to finite difference and hybrid difference methods. An error estimate is derived with the discrete norm. In the end, numerical examples are given to show the advantages of the proposed results (Mathematics Subject Classification: 65L11, 65L12, and 65L20).

Biorthogonal nonuniform B-spline wavelets based on a discrete norm

2009 ◽  
Vol 26 (4) ◽  
pp. 480-492 ◽  
Author(s):  
Rijing Pan ◽  
Zhiqiang Yao
Keyword(s):  
B Spline ◽  
Spline Wavelets ◽  
Discrete Norm

scholarly journals Lower-order equivalent nonstandard finite element methods for biharmonic plates

2021 ◽  
Author(s):  
Neela Nataraj ◽  
Carsten Carstensen
Keyword(s):  
Finite Element ◽  
Discontinuous Galerkin ◽  
Finite Element Methods ◽  
Biharmonic Equation ◽  
Input Function ◽  
Comparison Results ◽  
Sobolev Norms ◽  
Discrete Norm ◽  
Numer Anal ◽  
Nonconforming Methods

The popular (piecewise) quadratic schemes for the biharmonic equation based on triangles are the nonconforming Morley finite element, the discontinuous Galerkin, the C0    interior penalty, and the WOPSIP schemes. Those methods are modified in their right-hand side and then are quasi-optimal in their respective discrete norms. The smoother JI M  is defined for a piecewise smooth input function by a (generalized) Morley interpolation I M  followed by a companion operator J. An abstract framework for the error analysis in the energy, weaker and piecewise Sobolev norms for the schemes is outlined and applied to the biharmonic equation. Three errors are also equivalent in some particular discrete norm from [Carstensen, Gallistl, Nataraj: Comparison results of nonstandard P 2  finite element methods for the biharmonic problem, ESAIM Math. Model. Numer. Anal. (2015)] without data oscillations. This paper extends and unifies the work [Veeser, Zanotti: Quasioptimal nonconforming methods for symmetric elliptic problems, SIAM J. Numer. Anal. 56 (2018)] to the discontinuous Galerkin scheme and adds error estimates in weaker and piecewise Sobolev norms.

scholarly journals Some properties of orders of quaternion algebras with regard to the discrete norm

2016 ◽  
Vol 141 (3) ◽  
pp. 385-405
Author(s):  
Jan Horníček ◽  
Miroslav Kureš ◽  
Lenka Macálková
Keyword(s):  
Quaternion Algebras ◽  
Discrete Norm
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