M. Azaïez

TL;DR: In this article, open boundary conditions for incompressible Navier-Stokes equations, in the framework of velocity-correction methods, have been studied, and the standard way to enforce this type of boundary condition is described, followed by an adaptation of the one we proposed in [36] that provides higher pressure and velocity convergence rates in space and time for pressure correction schemes.

TL;DR: It is shown how the singular value decomposition underlying the (KL)-expansion is connected to the spectrum of some Gram matrices and that the derivation of the corresponding truncation error is related to the spectral properties of these GramMatrices which are structured matrices with low displacement ranks.

TL;DR: Improved Reduced Order Models (ROM) for convection-dominated flows are introduced and an efficient practical implementation of the stabilization term is suggested, where the stabilization parameter is approximated by the Discrete Empirical Interpolation Method (DEIM).

TL;DR: In this article, a fractional Jacobi-collocation spectral method for the second kind Volterra integral equations (VIEs) with weakly singular kernel was proposed and analyzed, and a detailed convergence analysis was carried out to derive error estimates of the numerical solution in both $L^{\infty}$- and weighted $L^{2}-norms.

TL;DR: In this article, the authors focus on the convergence analysis of the POD expansion for the parameterized solution of transient heat equations and prove that this expansion converges with exponential accuracy, uniformly if the conductivity coefficient remains within a compact set of positive numbers.