Paola Gervasio

Heterogeneous coupling by virtual control methods

Summary. The virtual control method, recently introduced to approximate elliptic and parabolic problems by overlapping domain decompositions (see [7–9]), is proposed here for heterogeneous problems. Precisely, we address the coupling of an advection equation with a diffusion-advection equation, with the aim of modelling boundary layers. We investigate both overlapping and non-overlapping (disjoint) subdomain decompositions. In the latter case, several cost functions are considered and a numerical assessment of our theoretical conclusions is carried out.

Algebraic fractional-step schemes with spectral methods for the incompressible Navier-Stokes equations

The numerical investigation of a recent family of algebraic fractional-step methods for the solution of the incompressible time-dependent Navier-Stokes equations is presented. These methods are improved versions of the Yosida method proposed in [A. Quarteroni, F. Saleri, A. Veneziani, Factorization methods for the numerical approximation of Navier-Stokes equations Comput. Methods Appl. Mech. Engrg. 188(1-3) (2000) 505-526; A. Quarteroni, F. Saleri, A. Veneziani, J. Math. Pures Appl. (9), 78(5) (1999) 473-503] and one of them (the Yosida4 method) is proposed in this paper for the first time. They rely on an approximate LU block factorization of the matrix obtained after the discretization in time and space of the Navier-Stokes system, yielding a splitting in the velocity and pressure computation. In this paper, we analyze the numerical performances of these schemes when the space discretization is carried out with a spectral element method, with the aim of investigating the impact of the splitting on the global accuracy of the computation.

Stabilized spectral element approximation for the Navier–Stokes equations

The conforming spectral element methods are applied to solve the linearized Navier–Stokes equations by the help of stabilization techniques like those applied for finite elements. The stability and convergence analysis is carried out and essential numerical results are presented demonstrating the high accuracy of the method as well as its robustness.

Multimodels for incompressible flows

Abstract. The Navier—Stokes equations for incompressible fluids are coupled to models of reduced complexity, such as Oseen and Stokes, and the corresponding transmission conditions are investigated. A mathematical analysis of the corresponding problems is carried out. Numerical results obtained by finite elements and spectral elements are shown on several flow fields of physical interest.

Finite-Element Preconditioning of G-NI Spectral Methods

Several old and new finite-element preconditioners for nodal-based spectral discretizations of

THE INTERFACE CONTROL DOMAIN DECOMPOSITION (ICDD) METHOD FOR ELLIPTIC PROBLEMS

-\Delta u=f

Heterogeneous mathematical models in fluid dynamics and associated solution algorithms

in the domain

Algebraic Fractional-Step Schemes for Time-Dependent Incompressible Navier---Stokes Equations

\Omega=(-1,1)^d

Extended variational formulation for heterogeneous partial differential equations

(

The Spectral Projection Decomposition Method for Elliptic Equations in Two Dimensions

d=2