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References Blakemore, D. (1992). Understanding Utterances. An Introduction to Pragmatics . Oxford UK and Cambridge USA: Blackwell. Corder, S.P. (1967). The significance of learner’s errors. International Review of Applied Linguistics in Language Teaching 5 (4), 161–170. Corder, S.P. (1972). Die Rolle der Interpretation bei der Untersuchung von Schülerfehlern. In G. Nickel (Ed.), Fehlerkunde. Beiträge zur Fehleranalyse, Fehlerbewertung und Fehlertherapie (pp. 38–50). Berlin: Cornelsen und Klasing. Corder, S.P. (1981). Error Analysis and Interlanguage. Oxford

DOI 10.1515/cmam-2014-0021 | Comput. Methods Appl. Math. 2014; 14 (4):419–427 Research Article Fioralba Cakoni, Peter Monk and Jiguang Sun Error Analysis for the Finite Element Approximation of Transmission Eigenvalues Abstract: In this paper we consider the transmission eigenvalue problem corresponding to acoustic scatter- ing by a bounded isotropic inhomogeneous object in two dimensions. This is a non-self-adjoint eigenvalue problem for a quadratic pencil of operators. In particular we are concernedwith theoretical error analysis of a nite elementmethod for

Russ. J. Numer. Anal. Math. Modelling, Vol. 17, No. 1, pp. 071–097 (2002) c VSP 2002 On error analysis in data assimilation problems F.-X. Le DIMET, P. NGNEPIEBA, and V. SHUTYAEV† Abstract — We consider the data assimilation problem for a nonlinear evolution model to identify the initial condition. We derive an equation for the error of the optimal solution through the errors of the input data, which is based on the Hessian of a misfit functional, and study the solvability of the error equation. Fundamental control functions are used for error analysis. We

J. Inverse Ill-Posed Probl. 20 (2012), 411–428 DOI 10.1515/ jip-2012-0006 © de Gruyter 2012 A posteriori error analysis for unstable models Anatoly B. Bakushinsky, Alexandra Smirnova and Hui Liu Abstract. In this paper, we consider the possibility of a posteriori error estimates for linear and nonlinear ill-posed operator equations. Given an auxiliary finite-dimensional problem ˆ.w/ D 0, ˆ W Dˆ EN ! EM that approximates the original infinite model F.x/ D 0, F W DF X ! Y with a certain level of accuracy, we try to estimate the distance between z, an approximate

We present a solution of the problem of convergence of HPSTM. The maximum absolute truncation error of the series solution is estimated in Table 1 and Table 2 . As an application we apply the HPSTM on Newell-Whitehead-Segel equation and Fisher’s equation to obtain the approximate solution. The results obtained regarding the convergence and error analysis of HPSTM are verified by examples.The numerical results in the Table 1 and Table 2 shows that the results are closed to the exact ones. Table 1 Numerical solution when λ = 2 x U exact U HPSTM = s 5

, the OMM cannot be implemented with extreme slim range step sizes or in waveguides with rapidly changing parts, where the marching schemes with fast Fourier transform [ 14 , 15 ] or the downward extrapolation method [ 16 ] is usually more efficient. In spite of quite a number of contributions dealing with the OMM, limited error analysis work has been done rigorously for the OMM. Therefore, we discuss theoretical aspects related to error accumulations of the OMM to reveal the underlying reasons for the above computing features. First, we introduce a measure of the

analyzed for magnetic induction equation in the presence of resistivity. On the other hand, an exactly divergence free scheme is studied recently by Yang and Li [ 24 ] in Cartesian co-ordinates and, subsequently, error estimates are also obtained through the energy methods. In this paper, we will focus on the error analysis of the DG scheme for ( 1.3 ). More precisely, we will carry out the convergence analysis of the stabilized DG scheme presented in [ 21 ]. We obtain the semi-discretization in space using the discontinuous Galerkin (DG) methods and time discretization

typically used in computational fluid dynamics. The main aim of this paper is to present error analysis of two finite element-type approximations of the problem (1.2) . In particular, we combine the lowest order Taylor–Hood finite element discretization of the flow part (piecewise quadratic velocity and piecewise linear pressure) with either piecewise linear finite elements or finite volumes for the deformation gradient. The paper is organized as follows. In Section 2 we introduce space discretizations of (1.2) . The main result on convergence rates is stated in

, Berlin, 2007. Translated and revised from the 3rd (2005) German edition by Martin Stynes. [43] V. Mehrmann and J.J. Stolwijk. Error analysis for the Euler equations in purely algebraic form. Technical Report 2015/06, TU Berlin, Institut für Mathematik, 2015.

J. Numer. Math., Vol. 17, No. 1, pp. 27–44 (2009) DOI 10.1515/ JNUM.2009.003 c© de Gruyter 2009 Unified framework for an a posteriori error analysis of non-standard finite element approximations of H(curl)-elliptic problems C. CARSTENSEN∗ and R. H. W. HOPPE†‡ Dedicated to the sixtieth anniversary of Rolf Rannacher Abstract — A unified framework for a residual-based a posteriori error analysis of standard con- forming finite element methods as well as non-standard techniques such as nonconforming and mixed methods has been developed in [20–24]. This paper provides