Ngoc Cuong Nguyen

TL;DR: Barrault et al. as discussed by the authors presented an efficient reduced-basis discretization procedure for partial differential equations with nonaffine parameter dependence, replacing non-affine coefficient functions with a collateral reducedbasis expansion, which then permits an affine offline-online computational decomposition.

TL;DR: In this paper, the authors extended the reduced-basis approximations developed earlier for linear elliptic and parabolic partial differential equations with affine parameter dependence to problems in volving.

TL;DR: In this paper, the authors present hybridizable discontinuous Galerkin methods for the numerical solution of steady and time-dependent nonlinear convection-diffusion equations, which are devised by expressing the approximate scalar variable and corresponding flux in terms of an approximate trace of the scalar variables and then explicitly enforcing the jump condition of the numerical fluxes across the element boundary.

TL;DR: In this article, Lagrangian interpolation is used to approximate general functions by finite sums of well chosen, pre-defined, linearly independent interpolating functions; it is much simpler to implement than determining the best fits with respect to some Banach (or even Hilbert) norm.

TL;DR: An implicit high-order hybridizable discontinuous Galerkin method for the steady-state and time-dependent incompressible Navier-Stokes equations and displays superconvergence properties that allow it to use the above-mentioned optimal convergence properties to define an element-by-element postprocessing scheme to compute a new and better approximate velocity.