Adaptive methods
We develop and investigate various adaptive discretization schemes for the numerical solution of elliptic and parabolic problems. One line of investigations concerns 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. Adaptive methods have been widely studied in the recent past for stationary problems. Nevertheless, the unsteady context, where the spatial and the temporal discretizations mix each other in a very complex way, provides a framework in which adaptive methods can provide a very large improvement of computational performances and accuracy of the solution.