Averaging of gradient in the space of linear triangular and bilinear rectangular finite elements
| Autor: | Josef Dalík, Vaclav Valenta |
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| Rok vydání: | 2013 |
| Předmět: |
General Mathematics
Mathematical analysis Bilinear interpolation Triangulation (social science) averaging partial derivatives linear triangular and bilinear rectangular finite element Directional derivative nonobtuse regular triangulation Space (mathematics) Finite element method Domain (mathematical analysis) Number theory adaptive solution of elliptic differential problems in 2d QA1-939 A priori and a posteriori Mathematics 65d25 a posteriori error estimator |
| Zdroj: | Open Mathematics, Vol 11, Iss 4, Pp 597-608 (2013) |
| ISSN: | 2391-5455 |
| DOI: | 10.2478/s11533-012-0159-7 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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