Under mild additional assumptions this paper constructs quasi -interpolants in the form f h (x) = +1 X j= 1 f(hj)' h x h j ; x 2 IR; h > 0 (0.1) with approximation order ` 1, where ' h (x) is a linear combination of translates (x jh) of a function in C ` (IR). Thus the order of convergence of such operators can be pushed up to a limit that only depends on the smoothness of the function . This a...

A conforming finite element method on polygonal meshes is introduced which handles hanging nodes naturally. Ansatz functions are defined to fulfil the homogeneous PDE locally and they are treated by means of local boundary integral equations. Using a quasi-interpolation operator of Clément type a residual-based error estimate is obtained. This a posteriori estimator can be used to rate the accu...

We study the description by means of J-functional logarithmic interpolation spaces (A0, A1) 1, q, A in category p-normed quasi-Banach couples (0 < p ? 1). When is a Banach couple, it known that changes depending on relationship between q and A. In our more general setting, parameter also has an important role as results show.

In this paper, we propose a method to deal with numerical integral by using two kinds of C quasi-interpolation operators on the bivariate spline space, and also discuss the convergence properties and error estimates. Moreover, the proposed method is applied to the numerical evaluation of 2-D singular integrals. Numerical experiments will be carried out and the results will be compared with some...