We analyze the Ritz–Galerkin method for symmetric eigenvalue problems and prove a priori eigenvalue error estimates. For a simple eigenvalue, we prove an error estimate that depends mainly on the approximability of the corresponding eigenfunction and provide explicit values for all constants. For a multiple eigenvalue we prove, in addition, apparently the first truly a priori error estimates th...

the aim of this work is to investigate the variational discretization and mixed finite element methods for optimal control problem governed by semi linear parabolic equations with integral constraint. the state and co-state are approximated by the lowest order raviart-thomas mixed finite element spaces and the control is not discreted. optimal error estimates in l2 are established for the state...

We apply a discrete network approximation to the problem of the effective conductivity of the high contrast, highly packed composites. The inclusions are irregularly (randomly) distributed in the hosting medium, so that a significant fraction of them may not participate in the conducting spanning cluster. For this class of inclusion distributions we derive a discrete network approximation and o...

Abstract. This paper is concerned with the computation of numerical discretization error for uncertainty quantification. An a posteriori error formula is described for a functional measurement of the solution to a scalar advection equation that is estimated by finite volume approximations. An exact error formula and computable error estimate are derived based on an abstractly defined approximat...

In this paper we present an a priori error estimate of the Runge-Kutta discontinuous Galerkin method for solving symmetrizable conservation laws, where the time is discretized with the third order explicit total variation diminishing Runge-Kutta method and the finite element space is made up of piecewise polynomials of degree k ≥ 2. Quasi-optimal error estimate is obtained by energy techniques,...

A Posteriori Error Analysis in the maximum norm for a penalty finite element method for the time-dependent obstacle problem Abstract. We consider nite element approximation of the parabolic obstacle problem. The analysis is based on a penalty formulation of the problem where the penalisation parameter is allowed to vary in space and time. We estimate the penalisation error in terms of the penal...

In this article we introduce a new locking-free completely discontinuous formulation for Reissner–Mindlin plates that combines the discontinuous Galerkin methods with weakly over-penalized techniques. We establish a new discrete version of Helmholtz decomposition and some important residual estimates. Combining the residual estimates with enriching operators we derive an optimal a priori error ...

An adaptive online flux-linkage estimation method for the sensorless control of switched reluctance motor (SRM) drive is presented in this paper. Sensorless operation is achieved through a binary observer based algorithm. In order to avoid using the look up tables of motor characteristics, which makes the system, depends on motor parameters, an adaptive identification algorithm is used to estim...