Triangulations, and more precisely meshes, are at the heart of many problems relating to a wide variety of scientific disciplines, and in particular numerical simulations of all kinds of physical phenomena. In numerical simulations, the functional spaces of approximation used to search for solutions are defined from meshes, and in this sense these meshes play a fundamental role. This strong link between meshes and functional spaces leads us to consider advanced simulation methods in which the meshes are adapted to the behaviors of the underlying physical phenomena. This book presents the basic elements of this vision of meshing. These mesh adaptations are generally governed by a posteriori error estimators representing an increase of the error with respect to a size or metric. Independently of this metric of calculation, compliance with a geometry can also be calculated using a so-called geometric metric. The notion of mesh thus finds its meaning in the metric of its elements.

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Paul Louis George is Director of Research at the French Institute for Research in Computer Science and Automation (Inria) and one of the most internationally recognized experts in meshing. Houman Borouchaki is Professor at the University of Technology of Troyes (UTT) in France. He is an expert on meshing problems, geometric modeling and applications in solid mechanics. Fr�d�ric Alauzet is a researcher at Inria, both with particular expertise in meshing adaptation, error estimators, resolution methods (advanced solvers in fluid mechanics) and remeshing methods. Adrien Loseille is a researcher at Inria, both with particular expertise in meshing adaptation, error estimators, resolution methods (advanced solvers in fluid mechanics) and remeshing methods. Patrick Laug is a researcher at Inria with particular expertise in geometric modeling and the generation of curve and surface meshes. Lo�c Mar�chal, a long-time collaborator at Inria as an engineer, is an essential reference on hexahedra.

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