| Autor: |
Dalík, Josef, Valenta, Václav |
| Zdroj: |
Central European Journal of Mathematics; Apr2013, Vol. 11 Issue 4, p597-608, 12p |
| Abstrakt: |
An averaging method for the second-order approximation of the values of the gradient of an arbitrary smooth function u = u( x, x) at the vertices of a regular triangulation T composed both of rectangles and triangles is presented. The method assumes that only the interpolant Π[ u] of u in the finite element space of the linear triangular and bilinear rectangular finite elements from T 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. [ABSTRACT FROM AUTHOR] |
| Databáze: |
Complementary Index |
| Externí odkaz: |
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