Spectral and h-p type finite element methods
Current activities concern the development and analysis of optimal low-order preconditioners for Discontinuous-Galerkin spectral element discretizations of elliptic problems. Other interests focus on the definition of adaptive algorithms for Fourier and Legendre discretizations, and the study of their properties of convergence and optimality in the framework of nonlinear approximation theory. Recent applications deal with hydrodynamic stability problems investigated by means of spectral Legendre numerical schemes.