On numerical regularity of the face-to-face longest-edge bisection algorithm for tetrahedral partitions
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Quadrilateral and triangular elements with curved edges are developed in the framework of spectral, discontinuous, hybrid control-volume/finite-element method for elliptic problems. In order to accommodate hybrid meshes, encompassing both triangular and quadrilateral elements, one single mapping is used. The scheme is applied to two-dimensional problems with discontinuous, anisotropic diffusion coefficients, and the exponential convergence of the method is verified in the presence of curved geometries.