Averaging of Gradients in Vertices of Triangulations

For a conforming shape-regular triangulation T-h without obtuse angles of a bounded polygonal domain Omega subset of R-2, a weighted averaging operator relating a high-order approximation W[z, Pi(h)(u)](a) of the directional derivative partial derivative u/partial derivative z(a) to a unit vector z, inner or so-called semi-inner vertex a of T-h and to the interpolant Pi(h)(u) of a smooth function u in the vertices of T-h has been presented in [3]. The interpolant Pi(h)(u) is continuous on (Omega) over bar and linear on all triangles from T-h. In this paper, the problem of how to find effective procedures for such high-order approximations of the gradient del u(a) by weighted averaging is studied.