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Detail publikace
DALÍK, J. VALENTA, V.
Originální název
Averaging of gradient in the space of linear triangular and bilinear rectangular finite elements
Typ
článek v časopise - ostatní, Jost
Jazyk
angličtina
Originální abstrakt
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.
Klíčová slova
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
Autoři
DALÍK, J.; VALENTA, V.
Rok RIV
2013
Vydáno
1. 1. 2013
Nakladatel
VERSITA
Místo
Velká Británie
ISSN
1895-1074
Periodikum
CENT EUR J MATH
Ročník
4
Číslo
11
Stát
Polská republika
Strany od
597
Strany do
608
Strany počet
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" }