Bounds of Interpolation Error for Arbitrary Narrow Quadrilateral Quasi-Wilson Element

Based on the construction of reference e le ment and bilinear transformation, a quasi-Wilson element for arbitrary narrow q uadrilateral is presented. Using the interpolation Theorem for narrow quadrilate ral isoparametric finite element and related methods, the bounds of interpolatio n error for arbitrary narrow quadrilateral quasi-Wilson element are obtained in case when the condition ρ K/h K≥σ 0】0 is not satisfied, where h K is the diameter of the element K and ρ K is the diameter of an ins cribed circle in K. The interpolation error is O(h2 K) in the L2( K)-norm and O(h K) in the H1(K) -norm provided that the in terpolated function belongs to H2(K).

Calculation of Space NURBS Curve Interpolation Error

Aiming at the problem of low accuracy of interpolation error calculation of existing NURBS curves, an approximate method for the distance between a point and a NURBS interpolation curve is proposed while satisfying the accuracy of the solution. Firstly, the minimum parameter interval of the node vector corresponding to the data point under test in the original data point sequence is determined, and the parameter interval is subdivided according to the corresponding step size, and the corresponding parameter value is obtained. Secondly, the distance from the measured point to the NURBS curve is calculated, and the nearest distance is found out. The node interval is subdivided again on one side of the nearest distance. Finally, the distance between the data point to be measured and each subdivision point is calculated again, and the minimum distance is taken as the interpolation error between the point and the NURBS curve. The simulation results of actual tool position data show that this method can more accurately obtain the error of spatial NURBS interpolation curve.

High accuracy NURBS interpolation for five-axis machine of table-rotating/spindle-tilting type

In this paper, the definition of NURBS curve and a speed-controlled interpolation in which the feed rate is automatically adjusted in order to meet the specified chord error limit were discussed. Besides those, a definition of linear interpolation error of post-processed data was proposed, which should be paid more attention to because it will not only reduce quality of the surface but also may cause interference and other unexpected trouble. In order to control the error, a robust algorithm was proposed, which successfully met a desired error limit through interpolating some essential CL data. The excellence of the proposed algorithm, in terms of its reliability and self-adaptiveness, has been proved by simulation results.

Anisotropic Interpolation Error Estimates of a Nonconforming Element

The main aim of this paper is to study the local anisotropic interpolation error estimates. We show that the interpolation of a nonconforming element satisfy the anisotropic property for both the second and fourth order problems.

ERROR BOUNDS IN PERIODIC QUARTIC SPLINE INTERPOLATION

In this paper we develop periodic quartic spline interpolation theory which,in general,gives better fus to continuous functions than does the existing quintic spline interpolation theory.The main theorem of the paper is to establish that r=0,1,2,3.Also,the nanperiodic cases cannot be constructed empoly-ing the methodology of this paper because that will involve several other end conditions entirely different than(1,10).

OPTIMAL ERROR BOUNDS FOR THE CUBIC SPLINE INTERPOLATION OF LOWER SMOOTH FUNCTIONS(1)

In this paper,the kernel of the cubic spline interpolation is given.An optimal error bound for the cu- bic spline interpolation of lower smooth functions is obtained.

UNIFORM APPROXIMATION OF ENTIRE FUNCTIONS OF SLOW GROWTH ON COMPACT SETS

In the present paper, we study the polynomial approximation of entire functions of several complex variables. The characterizations of generalized order and generalized type of entire functions of slow growth are obtained in terms of approximation and interpolation errors.

Sample based 3D face reconstruction from a single frontal image by adaptive locally linear embedding

In this paper, we propose a highly automatic approach for 3D photorealistic face reconstruction from a single frontal image. The key point of our work is the implementation of adaptive manifold learning approach. Beforehand, an active appearance model (AAM) is trained for automatic feature extraction and adaptive locally linear embedding (ALLE) algorithm is utilized to reduce the dimensionality of the 3D database. Then, given an input frontal face image, the corresponding weights between 3D samples and the image are synthesized adaptively according to the AAM selected facial features. Finally, geometry reconstruction is achieved by linear weighted combination of adaptively selected samples. Radial basis function (RBF) is adopted to map facial texture from the frontal image to the reconstructed face geometry. The texture of invisible regions between the face and the ears is interpolated by sampling from the frontal image. This approach has several advantages: (1) Only a single frontal face image is needed for highly automatic face reconstruction; (2) Compared with former works, our reconstruction approach provides higher accuracy; (3) Constraint based RBF texture mapping provides natural appearance for reconstructed face.

Modifying the intensity distribution by assessing the reliability

This article presents an application of a procedure to modify the intensity distribution by assessing the reliability. There are two potential possibilities that may influence the intensity distribution： （1） For the interpolation error, we generate a measured grid across the calculation region. When the point to station spacing is 〈5 km, we consider the results precise; however, some points have less precision because these are farther from the corresponding stations. When the spacing is between 5 and 50 km, we consider the results imprecise and define a reliability factor that correlates with the distance. （2） Some records may have errors that result from local site conditions, equipment problems, or some disturbance such as lightning stroke, which will lead to some grid points having an incorrect intensity. We regress the attenuation relation for sites with abnormal intensities and consider the results to be accurate when the standard deviation （STD） is 〈σ and inaccurate when the STD is 〉 2σ. We then define a reliability factor to correlate with STD between σ and 2σ, such that the intensity distribution is in accord with both wave propagation theory and the investigation intensity.

ON THE ANISOTROPIC ACCURACY ANALYSIS OF ACMES NONCONFORMING FINITE ELEMENT

The main aim of this paper is to study the superconvergence accuracy analysis of the famous ACM＇s nonconforming finite element for biharmonic equation under anisotropic meshes. By using some novel approaches and techniques, the optimal anisotropic interpolation error and consistency error estimates are obtained. The global error is of order O（h^2）. Lastly, some numerical tests are presented to verify the theoretical analysis.

An H^m-conforming spectral element method on multi-dimensional domain and its application to transmission eigenvalues

We develop an Hm-conforming(m 1) spectral element method on multi-dimensional domain associated with the partition into multi-dimensional rectangles. We construct a set of basis functions on the interval [-1, 1] that are made up of the generalized Jacobi polynomials(GJPs) and the nodal basis functions.So the basis functions on multi-dimensional rectangles consist of the tensorial product of the basis functions on the interval [-1, 1]. Then we construct the spectral element interpolation operator and prove the associated interpolation error estimates. Finally, we apply the H2-conforming spectral element method to the Helmholtz transmission eigenvalues that is a hot problem in the field of engineering and mathematics.

CONVERGENCE ANALYSIS OF MORLEY ELEMENT ON ANISOTROPIC MESHES

The main aim of this paper is to study tile convergence of a nonconforming triangular plate element-Morley element under anisotropic meshes. By a novel approach, an explicit bound for the interpolation error is derived for arbitrary triangular meshes （which even need not satisfy the maximal angle condition and the coordinate system condition ）, the optimal consistency error is obtained for a family of anisotropically graded finite element meshes.

Fourier-Chebyshev spectral method for cavitation computation in nonlinear elasticity

A Fourier-Chebyshev spectral method is proposed in this paper for solving the cavitation problem in nonlinear elasticity. The interpolation error for the cavitation solution is analyzed, the elastic energy error estimate for the discrete cavitation solution is obtained, and the convergence of the method is proved. An algorithm combined a gradient type method with a damped quasi-Newton method is applied to solve the discretized nonlinear equilibrium equations. Numerical experiments show that the Fourier-Chebyshev spectral method is efficient and capable of producing accurate numerical cavitation solutions.

Spatially adaptive long-term semi-Lagrangian method for accurate velocity advection

We introduce a new advection scheme for fluid animation.Our main contribution is the use of long-term temporal changes in pressure to extend the commonly used semi-Lagrangian scheme further back along the time axis.Our algorithm starts by tracing sample points along a trajectory following the velocity field backwards in time for many steps.During this backtracing process,the pressure gradient along the path is integrated to correct the velocity of the current time step.We show that our method effectively suppresses numerical diffusion,retains small-scale vorticity,and provides better long-term kinetic energy preservation.

A New Triangular Spectral Element Method II: Mixed Formulation and hp-Error Estimates

Mixed triangular spectral element method using nodal basis on unstructured meshes is investigated in this paper.The method is based on equivalent first order system of the elliptic problem and rectangle-triangle transforms.It fully enjoys the ten-sorial structure and flexibility in handling complex domains by using nodal basis and unstructured triangular mesh.Different from the usual Galerkin formulation,the mixed form is particularly advantageous in this context,since it can avoid the singularity in-duced by the rectangle-triangle transform in the calculation of the matrices,and does not require the evaluation of the stiffness matrix.An hp a priori error estimate is pres-ented for the proposed method.The implementation details and some numerical exam-ples are provided to validate the accuracy and flexibility of the method.