Alberto Valli

Navier-Stokes equations for compressible fluids: global existence and qualitative properties of the solutions in the general case

We consider the equations which describe the motion of a viscous compressible fluid, taking into consideration the case of inflow and/or outflow through the boundary. By means of some a priori estimates we prove the existence of a global (in time) solution. Moreover, as a consequence of a stability result, we show that there exist a periodic solution and a stationary solution.

An optimal domain decomposition preconditioner for low-frequency time-harmonic Maxwell equations

The time-harmonic Maxwell equations are considered in the low-frequency case. A finite element domain decomposition approach is proposed for the numerical approximation of the exact solution. This leads to an iteration-by-subdomain procedure, which is proven to converge. The rate of convergence turns out to be independent of the mesh size, showing that the preconditioner implicitly defined by the iterative procedure is optimal. For obtaining this convergence result it has been necessary to prove a regularity theorem for Dirichlet and Neumann harmonic fields.

Robin-Robin Domain Decomposition Methods for the Stokes-Darcy Coupling

In this paper we consider a coupled system made of the Stokes and Darcy equations, and we propose some iteration-by-subdomain methods based on Robin conditions on the interface. We prove the convergence of these algorithms, and for suitable finite element approximations we show that the rate of convergence is independent of the mesh size

A domain decomposition approach for heterogeneous time-harmonic Maxwell equations

h

On the existence of stationary solutions to compressible Navier–Stokes equations

. Special attention is paid to the optimization of the performance of the methods when both the kinematic viscosity

Theory and Application of Steklov-Poincaré Operators for Boundary-Value Problems

\nu

Asymptotic Behaviour of the density for one-dimensional navier-stokes equations.

of the fluid and the hydraulic conductivity tensor

Coupling of viscous and inviscid Stokes equations via a domain decomposition method for finite elements

K

Coercive domain decomposition algorithms for advection-diffusion equations and systems

of the porous medium are very small.

A formulation of the eddy current problem in the presence of electric ports

The time-harmonic Maxwell equations for a composite medium which behaves like a conductor in one part and like a perfect insulator in the other one are considered. An existence and uniqueness theorem is proven for this degenerate problem in the case of Dirichlet boundary conditions. A finite element domain decomposition approach is then proposed for the numerical approximation of the exact solution. This leads to an iteration-by-subdomain procedure, where at each step a non-degenerate boundary value problem has to be solved in each subdomain. The convergence of these iterations is proven, and the rate of convergence turns out to be independent of the mesh size h, showing that the preconditioner implicitly defined by the iteration procedure is optimal.