Convergence and optimality of the adaptive Morley element method
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- Hu, J., Shi, Z. & Xu, J. Numer. Math. (2012) 121: 731. doi:10.1007/s00211-012-0445-0
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.