As problems encountered in physics and engineering become more and more demanding in terms of accuracy, computational cost and effciency, we are led to consider strategies to overcome these diffculties. To increase accuracy, a strategy consists in augmenting the order of the finite element discretisation space (this is called the p-method). But this strategy further increases the size of the problem by adding more degrees of freedom to the linear system to be solved. On the contrary, mesh optimisation (h-method and r-method ) can be used to reduce the size of the problem while keeping the error to a minimum, thus reducing computational cost without losing too much accuracy. In the litterature, many mesh adaptation algorithms exists for the linear case (p = 1) but few for the cases p > 1 . Our goal is to present a general framework to obtain optimal meshes while using a xed, arbitrary order, nite element discretisation. To do so, we shall dene a new a posteriori hierarchical error estimator depending solely on the solution of the finite element problem at hand and its reconstructed gradient. The mesh adaptation procedure can thus be used independently (as a black box) of the PDE. Altough the presentation will be
focused on the 2D case, some examples will be given for 3D mesh adaptation.
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 D. Pagnutti and C. Ollivier-Gooch. A generalized framework for high order anisotropic mesh adaptation. Comput. Struct., 87:670-679, June 2009.