FINITE ELEMENTS FOR THE ANALYSIS OF REISSNE-RMINDLIN PLATES WITH JOINT INTERPOLATION OF DISPLACEMENTS AND ROTATIONS (JIDR)

This paper proposes a method for creating finite elements with simultaneous approximation of functions corresponding to displacements and rotations. New triangular and quadrangular finite elements have been created, which can have additional nodes on the sides. No locking effect is observed for all the created elements. All created elements retain the existing symmetry of the design models. The results of numerical experiments are presented.

Simultaneous approximations to p-adic numbers and algebraic dependence via multidimensional continued fractions

Unlike the real case, there are not many studies and general techniques for providing simultaneous approximations in the field of p-adic numbers $$\mathbb Q_p$$ Q p . Here, we study the use of multidimensional continued fractions (MCFs) in this context. MCFs were introduced in $$\mathbb R$$ R by Jacobi and Perron as a generalization of continued fractions and they have been recently defined also in $$\mathbb Q_p$$ Q p . We focus on the dimension two and study the quality of the simultaneous approximation to two p-adic numbers provided by p-adic MCFs, where p is an odd prime. Moreover, given algebraically dependent p-adic numbers, we see when infinitely many simultaneous approximations satisfy the same algebraic relation. This also allows to give a condition that ensures the finiteness of the p-adic Jacobi–Perron algorithm when it processes some kinds of $$\mathbb Q$$ Q -linearly dependent inputs.

A High Order Accurate Finite Difference Method for the Drinfel’d–Sokolov–Wilson Equation

We analyse numerically the periodic problem and the initial boundary value problem of the Korteweg-de Vries equation and the Drindfeld–Sokolov–Wilson equation using the summation-by-parts simultaneous-approximation-term method. Two sets of boundary conditions are derived for each equation of which stability is shown using the energy method. Numerical analysis is done when the solution interacts with the boundaries. Results show the benefit of higher order SBP operators.

Simultaneous Approximation by a New Sequence of Integral Type Based on Two Parameters

This paper introduces a generalization sequence of positive and linear operators of integral type based on two parameters to improve the order of approximation. First, the simultaneous approximation is studied and a Voronovskaja-type asymptotic formula is introduced. Next, an error of the estimation in the simultaneous approximation is found. Finally, a numerical example to approximate a test function and its first derivative of this function is given for some values of the parameters.

A Low Dissipative and Stable Cell-Centered Finite Volume Method with the Simultaneous Approximation Term for Compressible Turbulent Flows

A simultaneous-approximation term is a non-reflecting boundary condition that is usually accompanied by summation-by-parts schemes for provable time stability. While a high-order convective flux based on reconstruction is often employed in a finite-volume method for compressible turbulent flow, finite-volume methods with the summation-by-parts property involve either equally weighted averaging or the second-order central flux for convective fluxes. In the present study, a cell-centered finite-volume method for compressible Naiver–Stokes equations was developed by combining a simultaneous-approximation term based on extrapolation and a low-dissipative discretization method without the summation-by-parts property. Direct numerical simulations and a large eddy simulation show that the resultant combination leads to comparable non-reflecting performance to that of the summation-by-parts scheme combined with the simultaneous-approximation term reported in the literature. Furthermore, a characteristic boundary condition was implemented for the present method, and its performance was compared with that of the simultaneous-approximation term for a direct numerical simulation and a large eddy simulation to show that the simultaneous-approximation term better maintained the average target pressure at the compressible flow outlet, which is useful for turbomachinery and aerodynamic applications, while the characteristic boundary condition better preserved the flow field near the outlet.

Simultaneous approximation of images applications to image and video compression

Given a set of images we propose an algorithm that approximates all images simultaneously. The algorithm finds the best common partition of the images' domain at each step, this is accomplished by maximizing an appropriate inner product. The algorithm is a pursuit algorithm constrained to build a tree, the optimization is done over a large dictionary of wavelet-like functions. The approximations are given by vector valued discrete martingales that converge to the input set of images. Several computational and mathematical techniques are developed in order to encode the information needed for the reconstruction. Properties of the algorithm are illustrated through many examples, comparisons with JPEG2000 and MPEG4-3 are also provided.

Simultaneous approximation of images applications to image and video compression

Given a set of images we propose an algorithm that approximates all images simultaneously. The algorithm finds the best common partition of the images' domain at each step, this is accomplished by maximizing an appropriate inner product. The algorithm is a pursuit algorithm constrained to build a tree, the optimization is done over a large dictionary of wavelet-like functions. The approximations are given by vector valued discrete martingales that converge to the input set of images. Several computational and mathematical techniques are developed in order to encode the information needed for the reconstruction. Properties of the algorithm are illustrated through many examples, comparisons with JPEG2000 and MPEG4-3 are also provided.