Abstract
In this paper we present a unified description of new spectral bases suitable for high-order hp finite element discretizations on hybrid two-dimensional meshes consisting of triangles and quadrilaterals. All bases presented are for C0 continuous discretizations and are described both as modal and as mixed modal-nodal expansions. General Jacobi polynomials of mixed weights are employed that accommodate automatic exact numerical quadratures, generalized tensor products, and variable expansion order in each element. The approximation properties of the bases are analyzed in the context of the projection, linear advection, and diffusion operators.
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