On the error bounds of nonconforming finite elements |
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| Authors: | ShiPeng Mao ZhongCi Shi |
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| Institution: | 1. The State Key Laboratory of Scientific and Engineering Computing, Institute of Computational Mathematics and Scientific/Engineering Computing, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China
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| Abstract: | We prove that the error estimates of a large class of nonconforming finite elements are dominated by their approximation errors, which means that the well-known Cea’s lemma is still valid for these nonconforming finite element methods. Furthermore, we derive the error estimates in both energy and L 2 norms under the regularity assumption u ∈ H 1+s (Ω) with any s > 0. The extensions to other related problems are possible. |
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