Abstract This paper studies the problem of construction of optimal quadrature formulas in the sense of Sard in the space ( ) 2 (0,1) m L . In this paper the quadrature sum consists of values of the integrand and its first derivative at nodes. The coefficients of optimal quadrature formulas are found and the norm of the optimal error functional is calculated for arbitrary natural number 1 N m ≥ ...

In earlier work we have studied a method for discretization in time of a parabolic problem, which consists of representing the exact solution as an integral in the complex plane and then applying a quadrature formula to this integral. In application to a spatially semidiscrete finite-element version of the parabolic problem, at each quadrature point one then needs to solve a linear algebraic sy...

A singularly perturbed reaction-diiusion equation in two dimensions is considered. We assume analyticity of the input data, i.e., the boundary of the domain is an analytic curve and the right hand side is analytic. We show that the hp version of the nite element method leads to robust exponential convergence provided that one layer of needle elements of width O(p") is inserted near the domain b...

We use the informational approach of Traub and Wozniakowski [9] to study the variational form of the second order elliptic Dirichlet problem Lu = f on ü C RN. For /e Hr(Q), where r> -1, a quasi-uniform finite element method using n linear functional Jaf^i nas T7'(ß)-norm error 0(n~<r+1)/'v). We prove that it is asymptotically optimal among all methods using any information consisting of any n l...

The subject of this work is the application of fully discrete Galerkin finite element methods to initial-boundary value problems for linear partial integro-differential equations of parabolic type. We investigate numerical schemes based on the Padé discretization with respect to time and associated with certain quadrature formulas to approximate the integral term. A preliminary error estimate i...

Piezoelectric materials, due to their electromechanical coupling properties, are widely used as actuators and sensors in intelligent structures control vibrations bends of multilayer sheets with piezoelectric layers. In this paper, the response free a composite shell new Generalized Differential Quadrature Method (GDQM) for different boundary conditions is investigated. The governing equations ...

Efficient numerical algorithms are developed and analyzed that implementmultilevel preconditioners for the solution of the quadrature finite element Galerkin approximation of the biharmonic Dirichlet problem. The quadrature scheme is formulated using the Bogner-Fox-Schmit rectangular element and the product two-point Gaussian quadrature. The proposed additive and multiplicative preconditioners ...

The effect of the linear and nonlinear properties beam's material on dynamic behavior a structure under different kinematic influences is investigated. With an account for viscoelastic material, problem consideration reduced to system small-order or integro-differential equations by selection coordinate functions satisfying geometric boundary conditions; solved averaging method using quadrature...

The element-free Galerkin method is employed for two-dimensional analysis of steady-state heat transfer. The unknown response of the system, i.e. temperature is approximated using the moving least squares technique. Numerical integration of governing simultaneous system of equations is performed by Gauss quadrature and new modified nodal integration techniques. Numerical examples and tests have...