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

• Autorzy: Josef Dalík , Václav Valenta
• Języki publikacji: EN

Abstrakty

EN

An averaging method for the second-order approximation of the values of the gradient of an arbitrary smooth function u = u(x 1, x 2) at the vertices of a regular triangulation T h composed both of rectangles and triangles is presented. The method assumes that only the interpolant Πh[u] of u in the finite element space of the linear triangular and bilinear rectangular finite elements from T h 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.

Słowa kluczowe

EN

Linear triangular and bilinear rectangular finite element; Nonobtuse regular triangulation; Averaging partial derivatives; A posteriori error estimator; Adaptive solution of elliptic differential problems in 2D

Kategorie tematyczne

• 65D25: Numerical differentiation

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2013
• Tom: 11
• Numer: 4
• Strony: 597-608

Daty

wydano

2013-04-01

online

2013-01-29

Twórcy

autor

Josef Dalík

• Brno University of Technology

autor

Václav Valenta

• Brno University of Technology

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-012-0159-7