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DALÍK, J. VALENTA, V.
Original Title
Averaging of gradient in the space of linear triangular and bilinear rectangular finite elements
Type
journal article - other
Language
English
Original Abstract
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.
Keywords
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
Authors
DALÍK, J.; VALENTA, V.
RIV year
2013
Released
1. 1. 2013
Publisher
VERSITA
Location
Velká Británie
ISBN
1895-1074
Periodical
CENT EUR J MATH
Year of study
4
Number
11
State
Republic of Poland
Pages from
597
Pages to
608
Pages count
12
BibTex
@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" }