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By Alspach B., Xu M.Y.

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An edge-flip on ab will remove the two faces abc and bad and replace them with two new faces cdb and dca. As a result, edge ab is replaced by edge cd. In our method, we want to flip ab if the new triangles are “better” than the old ones with regard to either geometry approximation or mesh quality. Given an edge ab in T , we check if ab needs to be flipped if one of the following two conditions are met: (a) geometric approximation, either face abc or face bad is inverted; (b) mesh quality both abc and bad are not inverted and the smallest 6dangle of the two new faces (cdb and dca) is larger than the smallest 6d-angle of abc and bad.

Tk /, the last term in (16) turns out to be zero. K/ ; where the constant C does not depend on the aspect ratio sK of K. Then, we employ (17) together with estimate (8) and Lemma 2 with ˇ1 D 21;K , ˇ2 D 22;K , 54 M. Artina et al. uh /. w; z/. Mimicking the considerations in [5], we choose w D uh and z D vh . vh /: (19) Anisotropic Adapted Meshes for Brittle Fractures Under Plane-Strain Conditions 55 Remark 2 Although in this work we deal with a specific case of linear elasticity constitutive law, we do believe that it is possible to extend the a posteriori analysis to a more general model, for instance, the one recently introduced in [9].

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1/2-Transitive Graphs of Order 3p by Alspach B., Xu M.Y.

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