Superconvergence of tetrahedral quadratic finite elements for a variable coefficient elliptic equation |
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| Authors: | Jinghong Liu Gui Hu Qiding Zhu |
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| Affiliation: | 1. Department of Fundamental Courses, Ningbo Institute of Technology Zhajiang University, Ningbo 315100, China;2. Department of Fundamental Experiments, Hunan College of Information, Changsha 410200, China;3. Department of Mathematics, College of Mathematics and Computer Science, Hunan Normal University, Changsha 410081, China |
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| Abstract: | For a variable coefficient elliptic boundary value problem in three dimensions, using the properties of the bubble function and the element cancelation technique, we derive the weak estimate of the first type for tetrahedral quadratic elements. In addition, the estimate for the W1,1‐seminorm of the discrete derivative Green's function is also given. Finally, we show that the derivatives of the finite element solution uh and the corresponding interpolant Π2u are superclose in the pointwise sense of the L∞‐norm. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013 |
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| Keywords: | discrete derivative Green's function superconvergence tetrahedral finite elements |
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