For the linear finite element solution to a linear elliptic model problem, we derive an error estimator based upon appropriate gradient recovery by local averaging. In contrast to popular variants like the ZZ estimator, our estimator contains some additional terms that ensure reliability also on coarse meshes. Moreover, the enhanced estimator is proved to be (locally) efficient and asymptotically exact whenever the recovered gradient is superconvergent. We formulate an adaptive algorithm that is directed by this estimator and illustrate its aforementioned properties, as well as their importance, in numerical tests.
A posteriori error estimators, gradient recovery by averaging, and superconvergence / A. Veeser, F. Fierro. - In: NUMERISCHE MATHEMATIK. - ISSN 0029-599X. - 103:2(2006 Apr), pp. 267-298.
A posteriori error estimators, gradient recovery by averaging, and superconvergence
A. VeeserPrimo
;F. FierroUltimo
2006
Abstract
For the linear finite element solution to a linear elliptic model problem, we derive an error estimator based upon appropriate gradient recovery by local averaging. In contrast to popular variants like the ZZ estimator, our estimator contains some additional terms that ensure reliability also on coarse meshes. Moreover, the enhanced estimator is proved to be (locally) efficient and asymptotically exact whenever the recovered gradient is superconvergent. We formulate an adaptive algorithm that is directed by this estimator and illustrate its aforementioned properties, as well as their importance, in numerical tests.Pubblicazioni consigliate
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