Faculty of Information Technology, BUT

Publication Details

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

DALÍK Josef and VALENTA Václav. Averaging of gradient in the space of linear triangular and bilinear rectangular finite elements. Central European Journal of Mathematics, vol. 2012, no. 1, pp. 1-16. ISSN 1895-1074.
Czech title
Výpočet průměrného gradientu v prostoru lineárních trojúhelnikových a bilineárních obdélníkových konečných prvků
Type
journal article
Language
english
Authors
Dalík Josef, doc. RNDr., CSc. (FCE BUT)
Valenta Václav, Ing. (DITS FIT BUT)
Keywords
Regular triangular and rectangular triangulation, bilinear rectangular finite element, averaging the partial derivatives, high-order approximation
Abstract
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.
Published
2012
Pages
1-16
Journal
Central European Journal of Mathematics, vol. 2012, no. 1, ISSN 1895-1074
Book
Central european journal of mathematics
BibTeX
@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"
}
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