New a posteriori error estimate and quasi-optimal convergence of the adaptive nonconforming Wilson element

• Autores: Jun Hu, Longlong Jiang, Zhongci Shi
• Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 265, Nº 1, 2014, págs. 173-186
• Idioma: inglés
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• Resumen

  • In this paper we establish the quasi-optimal convergence of the adaptive nonconforming Wilson element on the rectangular mesh. The main ingredients are a new a posteriori error estimator and a crucial observation that there is some special orthogonality between the conforming part and the nonconforming part in the energy inner product, which helps us to show the quasi-orthogonality and the discrete reliability. Finally we integrate these components in a usual way to achieve the quasi-optimal convergence.