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On a new edge-based gradient recovery technique


A. Fortin, GIREF, Département de mathématiques et de statistique, Pavillon Vachon, 1045 avenue de la Médecine, Université Laval, Québec, Canada, G1V 0A6.



A posteriori error estimation methods for mesh adaptation often require an accurate computation of the gradient of a Lagrange finite element solution. The precision of the error estimation is directly related to the accuracy of the recovered gradient. We therefore present in this communication a simple method for the evaluation of the gradient of a linear Lagrange finite element solution, and we show that it has significant advantages over existing methods of the same order. The proposed method requires the solution of a global linear system that can be solved by a preconditioned conjugate gradient method. An interesting feature is that it does not require any special treatment for boundary nodes contrarily to classical local patch recovery methods. Copyright © 2012 John Wiley & Sons, Ltd.