Spectral/hp least-squares finite element formulation for the Navier-Stokes equations
Journal of Computational Physics
Least-squares finite element models of two-dimensional compressible flows
Finite Elements in Analysis and Design
Journal of Computational Physics
Discontinuous Galerkin Methods Applied to Shock and Blast Problems
Journal of Scientific Computing
Discontinuous Galerkin methods applied to shock and blast problems
Journal of Scientific Computing
An eigen-based high-order expansion basis for structured spectral elements
Journal of Computational Physics
Bernstein-Bézier Finite Elements of Arbitrary Order and Optimal Assembly Procedures
SIAM Journal on Scientific Computing
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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.