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

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Dalík J., Valenta V.

Open Mathematics

2013

tom 11

nr 4

597-608

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.

Ograniczanie wyników

1 Open Mathematics

1 Dalík J.

1 Valenta V.

1 2013

Wyniki wyszukiwania

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