The main aim of this paper is to study the $ P_1 $ nonconforming finite element approximations of the variational inequality arisen from the Signorini problem. We describe the finite dimensional closed convex cone approximation in a meanvalue-oriented sense. In this way, the optimal convergence rate $ O(h) $ can be obtained by a refined analysis when the exact solution belongs to $ H^{2}(\Omega) $ without any assumption. Furthermore, we also study the optimal convergence for the case $ u\in H^{1+\nu}(\Omega) $ with $ \frac{1}{2}<\nu<1 $.
Citation: Mingxia Li, Dongying Hua, Hairong Lian. On $ P_1 $ nonconforming finite element aproximation for the Signorini problem[J]. Electronic Research Archive, 2021, 29(2): 2029-2045. doi: 10.3934/era.2020103
The main aim of this paper is to study the $ P_1 $ nonconforming finite element approximations of the variational inequality arisen from the Signorini problem. We describe the finite dimensional closed convex cone approximation in a meanvalue-oriented sense. In this way, the optimal convergence rate $ O(h) $ can be obtained by a refined analysis when the exact solution belongs to $ H^{2}(\Omega) $ without any assumption. Furthermore, we also study the optimal convergence for the case $ u\in H^{1+\nu}(\Omega) $ with $ \frac{1}{2}<\nu<1 $.
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Mingxia Li, Dongying Hua, Hairong Lian. On $ P_1 $ nonconforming finite element aproximation for the Signorini problem[J]. Electronic Research Archive, 2021, 29(2): 2029-2045. doi: 10.3934/era.2020103
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