Detail publikace
Averaging of gradient in the space of linear triangular and bilinear rectangular finite elements
Valenta Václav, Ing., Ph.D.
A posteriori error estimator; Adaptive solution of elliptic differential problems in 2D; Averaging partial derivatives; Linear triangular and bilinear rectangular finite element; Nonobtuse regular triangulation
An averaging method for the second-order approximation of the values of the gradient of an arbitrary smooth function u = u(x1, x2) at the vertices of a regular triangulation Th composed both of rectangles and triangles is presented. The method assumes that only the interpolant \PI_h[u] of u in the finite element space of the linear triangular and bilinear rectangular finite elements from Th is known. A complete analysis of this method is an extension of the complete analysis concerning the finite element spaces of linear triangular elements from [Dalík J., Averaging of directional derivatives in vertices of nonobtuse regular triangulations, Numer. Math., 2010, 116(4), 619-644]. The second-order approximation of the gradient is extended from the vertices to the whole domain and applied to the a posteriori error estimates of the finite element solutions of the planar elliptic boundary-value problems of second order. Numerical illustrations of the accuracy of the averaging method and of the quality of the a posteriori error estimates are also presented.
@article{BUT98047,
author="Josef {Dalík} and Václav {Valenta}",
title="Averaging of gradient in the space of linear triangular and bilinear rectangular finite elements",
journal="CENT EUR J MATH",
year="2013",
volume="4",
number="11",
pages="597--608",
issn="1895-1074"
}