Abstract
On a large class of two-dimensional anisotropic meshes, the inf-sup condition (stability) is proved for the triangular and quadrilateral finite element pairs suggested by Bernardi/Raugel and Fortin. As a consequence the pairs \({\cal P}_2-{\cal P}_0\), \({\cal Q}_2-{\cal P}_0\), and \({\cal Q}_2^\prime-{\cal P}_0\) turn out to be stable independent of the aspect ratio of the elements.
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Apel, T., Nicaise, S. The inf-sup condition for low order elements on anisotropic meshes. Calcolo 41, 89–113 (2004). https://doi.org/10.1007/s10092-004-0086-5
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DOI: https://doi.org/10.1007/s10092-004-0086-5