Bubble stabilization of Chebyshev-Legendre high-order element methods for the advection-diffusion equation (Q2812590)

The authors discuss the bubble stabilization of Chebyshev-Legendre high-order element methods for the advection-diffusion equation. They first provide some notations, definitions and some properties of the Chebyshev interpolation operator in terms of non-weighted Sobolev norms and provide uniform bounds of the global interpolation polynomials with respect to the global piecewise linear functions. The authors refer to \textit{C. Canuto} and \textit{G. Puppo} [Comput. Methods Appl. Mech. Eng. 118, No. 3--4, 239--263 (1994; Zbl 0847.76059)] for the bubble stabilized Chebyshev method and the general case. A complete analysis of lower-order preconditioner with computational evidences is provided.