Exponential convergence of mixed hp-DGFEM for the incompressible Navier–Stokes equations in ℝ2

In a polygon $\varOmega \subset \mathbb{R}^2$ we consider mixed $hp$-discontinuous Galerkin approximations of the stationary, incompressible Navier–Stokes equations, subject to no-slip boundary conditions. We use geometrically corner-refined meshes and $hp$ spaces with linearly increasing polynomial degrees. Based on recent results on analytic regularity of velocity field and pressure of Leray solutions in $\varOmega$, we prove exponential rates of convergence of the mixed $hp$-discontinuous Galerkin finite element method, with respect to the number of degrees of freedom, for small data which is piecewise analytic.

Atomic Hp spaces and their duals on open subsets of ℝd

We study atomic Hardy

Advances in Analysis

Princeton University's Elias Stein was the first mathematician to see the profound interconnections that tie classical Fourier analysis to several complex variables and representation theory. His fundamental contributions include the Kunze–Stein phenomenon, the construction of new representations, the Stein interpolation theorem, the idea of a restriction theorem for the Fourier transform, and the theory of Hp Spaces in several variables. Through his great discoveries, through books that have set the highest standard for mathematical exposition, and through his influence on his many collaborators and students, Stein has changed mathematics. Drawing inspiration from Stein's contributions to harmonic analysis and related topics, this book gathers papers from internationally renowned mathematicians, many of whom have been Stein's students. The book also includes expository papers on Stein's work and its influence.