An analysis of finite volume element method for solving the Signorini problem

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• 作者：Tie Zhang ; ^{ztmath@163.com" class="auth_mail" title="E-mail the corresponding author} ; Zheng Li
• 关键词：Finite volume element ; Signorini problem ; Optimal error estimate ; Superconvergence ; A posteriori error estimate
• 刊名：Applied Mathematics and Computation
• 出版年：2015
• 出版时间：1 November 2015
• 年：2015
• 卷：270
• 期：Complete
• 页码：830-841
• 全文大小：419 K

文摘

We propose and analyze the finite volume element method for solving the Signorini problem. The stability and the optimal H¹-convergence rate are given. Particularly, we establish a superclose interpolation estimate for the bilinear form of this method. Based on this estimate and the interpolation post-processing technique, we derive an $O\left(h^{\frac{3}{2}}\right)$-order superconvergence in the H¹-norm under a proper regularity condition. Finally, an asymptotically exact a posteriori error estimator also is given for the error ∥u−u_h∥₁$\parallel u-u_h{\parallel }_1$.