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Center for Nonlinear Studies |
I will present an overview of recent developments in spectral/hp element methods, first for deterministic problems and then for stochastic problems. Both continuous and discontinuous Galerkin methods will be presented and various versions that provide flexibility in applications will be discussed. In the second part of the talk, a new formulation based on spectral orthogonal functionals will be presented (the Generalized Polynomial Chaos method). Examples will be drawn from incompressible, compressible, and plasma flows, and also from microfluidics.