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Convergence and optimality of the adaptive Morley element method |
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| Authors: | Jun Hu Zhongci Shi Jinchao Xu |
| Institution: | 1. LMAM and School of Mathematical Sciences, Peking University, Beijing, 100871, People’s Republic of China 2. Institute of Computational Mathematics, Chinese Academy of Sciences, Beijing, 100080, People’s Republic of China 3. The School of Mathematical Sciences, Peking University, Beijing, People’s Republic of China 4. Department of Mathematics, Pennsylvania State University, University Park, PA, 16801, USA |
| Abstract: | This paper is devoted to the convergence and optimality analysis of the adaptive Morley element method for the fourth order elliptic problem. A new technique is developed to establish a quasi-orthogonality which is crucial for the convergence analysis of the adaptive nonconforming method. By introducing a new parameter-dependent error estimator and further establishing a discrete reliability property, sharp convergence and optimality estimates are then fully proved for the fourth order elliptic problem. |
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