Detail publikace

Averaging of gradient in the space of linear triangular and bilinear rectangular finite elements

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"
}