Publication Details
Averaging of gradient in the space of linear triangular and bilinear rectangular finite elements
Valenta Václav, Ing. (DITS FIT BUT)
Regular triangular and rectangular triangulation, bilinear rectangular finite element, averaging the partial derivatives, high-order approximation
We present the averaging method for the second-order approximations of the values of the gradient of an arbitrary smooth function u in the vertices of a triangulation T composed both of rectangles and triangles in general. The method assumes that the interpolant P[u] of u in the finite-element space related to the linear and bilinear finite elements on the triangles and rectangles from T is known only. The second-order approximation of the first partial derivatives is extended from the vertices to the whole domain and applied to the high-order aposteriori error estimates of the errors of the finite-element approximate solutions of the elliptic boundary-value problems for partial differential equations of second order.
@ARTICLE{FITPUB9871,
author = "Josef Dal\'{i}k and V\'{a}clav Valenta",
title = "Averaging of gradient in the space of linear triangular and bilinear rectangular finite elements",
pages = "1--16",
booktitle = "Central european journal of mathematics",
journal = "Central European Journal of Mathematics",
volume = 2012,
number = 1,
year = 2012,
ISSN = "1895-1074",
language = "english",
url = "https://www.fit.vut.cz/research/publication/9871"
}