Effect Of Quadrature Errors Research Articles

A NOTE ON THE PERTURBED LAX-MILGRAM PROBLEM

We deal with an error estimate of the perturbed Lax-Milgram problem with respect to the perturbation in the right-hand side. Two examples of perturbed problems in Sobolev spaces and their detailed analysis are given. The problem considered here is related to the effect of quadrature errors on the finite element solution, analyzed in Ciarlet \cite{ciarlet: 91}, Strang et al \cite{strang: 73}, Janik \cite{janik: 86} and Ko\l odziejczyk \cite{kolo: 89}. However, in contrast to these papers, where (very often) tedious analysis of the effect of quadrature errors of a product of two functions, is given, a different approach is used. We consider the error by {\it the exact integration} of the product of a projection of function $f$ and an element from subspace where we seek the approximate solutions. This simplifies analysis and, as indicated examples show, also gives not complicated formulae. The main characteristic of it is that numerical quadrature of a product of two functions can be interpreted as a quadrature with respect to only one function.

Electrical Model of Inside Sense Outside Drive Frame Micro-Gyroscope Including Quadrature Error and Coriolis Offset

Quadrature error and Coriolis offset are main errors of micro-gyroscopes which caused by manufacturing imperfections. They deteriorate the overall performance of micro-gyroscopes. For inside sense outside drive frame micro-gyroscope, quadrature error and Coriolis offset have their own characters. Based on the mechanical analysis of inside sense outside drive frame micro-gyroscope in imperfect condition, the dynamic equations of condition with quadrature error and Coriolis offset are investigated, and an equivalent electrical model with quadrature error and Coriolis offset is presented. It is convenient to observe the effect of quadrature error and Coriolis offset by equivalent electrical model simulating. Three conditions are simulated and compared. The results indicate that the Coriolis offset reduces the amplitude of instantaneous displacement to a very small extent. Its effect can be neglected. Quadrature error causes an error displacement with the amplitude much bigger than the prefect displacement’s amplitude. It is the overwhelming error in ISOD frame micro-gyroscope.

Solution of Helmholtz Equation in the Exterior Domain by Elementary Boundary Integral Methods

In this paper elementary boundary integral equations for the Helmholtz equation in the exterior domain, based on Green's formula or through representation of the solution by layer potentials, are considered. Even when the partial differential equation has a unique solution, for any given closed boundary I, these elementary boundary integral equations can be shown to be singular at a countable set of characteristic wavenumbers. Spectral properties and conditioning of the boundary integral operators and their discrete boundary element counterparts are studied near characteristic wavenumbers, with a view to assessing the suitability of these formulations for the solution of the exterior Helmholtz equation. Collocation methods are used for the discretisation of the boundary integral equations which are either of the Fredholm first kind, second kind, or hyper-singular type. The effect of quadrature errors on the accuracy of the discrete collocation methods is systematically investigated.

An Analysis of Quadrature Errors in Second-Kind Boundary Integral Methods

This paper considers the effect of quadrature errors on Galerkin methods for approximating the solution of second-kind Fredholm integral equations with weakly singular kernels defined on a smooth, closed surface in three dimensions. A quadrature strategy for Galerkin methods that use piecewise poly-nomials, both continuous and discontinuous, on a quadrilateral-based mesh is proposed. The error resulting from this further discretization is proved to be no larger than the original discretization error, and moreover, the amount of work needed to compute the resulting matrix for the corresponding linear system is shown to be proportional to the number of matrix entries.

Numerical Solution of Sigular Integral Equations Using Gauss-type Formulae I

Of concern here are the Gauss—Chebyshev formulae for numerical solution of singular integral equations of the Cauchy-type. The coefficient matrix of the linear sustem of algebraic equations corresponding to the dominant term term is shown to have an inverse, which is expressed in a neat, closed form. Using the norm of the inverse matrix, the effect of quadrature errors on the computed solution is estimated. Using Jackson's theorems on “best approximation”, convergence of the procedure is proved under favourable conditions. In the course of analysis, a number of identities involving the zeros of Chebyshev polynomials of first and second kind is obtained.

The Effect of Quadrature Errors on Finite Element Approximations for Second Order Hyperbolic Equations

The effects of numerical quadrature errors on finite element approximations to the solution of the mixed initial-boundary value problem for second order linear hyperbolic equations are studied. It is shown that the optimal $L^2 $- and $H^1 $-estimates may be recovered for certain classes of quadrature schemes.

The Effect of Quadrature Errors in the Computation of $L^2 $ Piecewise Polynomial Approximations

In this paper we investigate the $L^2 $ piecewise polynomial approximation problem. $L^2 $ bounds for the derivatives of the error in approximating sufficiently smooth functions by polynomial splines follow immediately from the analogous results for polynomial spline interpolation. We derive $L^2 $ bounds for the errors introduced by the use of two types of quadrature rules for the numerical computation of $L^2 $ piecewise polynomial approximations. These bounds enable us to present some asymptotic results and to examine the consistent convergence of appropriately chosen sequences of such approximations. Some numerical results are also included.

The effect of quadrature errors in the numerical solution of two-dimensional boundary value problems by variational techniques

The effect of quadrature errors in the numerical solution of two-dimensional boundary value problems by variational techniques

The effect of quadrature errors in the numerical solution of two-dimensional boundary value problems by variational techniques

The effect of quadrature errors in the numerical solution of two-dimensional boundary value problems by variational techniques

The effect of quadrature errors in the numerical solution of boundary value problems by variational techniques

The effect of quadrature errors in the numerical solution of boundary value problems by variational techniques

The effect of quadrature errors in the numerical solution of boundary value problems by variational techniques

The effect of quadrature errors in the numerical solution of boundary value problems by variational techniques