A new cubic nonconforming finite element on rectangles |
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| Authors: | Zhaoliang Meng Zhongxuan Luo Dongwoo Sheen |
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| Institution: | 1. School of Mathematical Sciences, Dalian University of Technology, Dalian, China;2. School of Software, Dalian University of Technology, Dalian, China;3. Department of Mathematics & Interdisciplinary Program in Computational Sciences & Technology, Seoul National University, Seoul, Korea |
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| Abstract: | A new nonconforming rectangle element with cubic convergence for the energy norm is introduced. The degrees of freedom (DOFs) are defined by the 12 values at the three Gauss points on each of the four edges. Due to the existence of one linear relation among the above DOFs, it turns out the DOFs are 11. The nonconforming element consists of  . We count the corresponding dimension for Dirichlet and Neumann boundary value problems of second‐order elliptic problems. We also present the optimal error estimates in both broken energy and  norms. Finally, numerical examples match our theoretical results very well. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 691–705, 2015 |
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| Keywords: | nonconforming finite element optimal error estimates quadrilateral mesh |
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