Scientific computing is a very broad subject. The contents of the book under review can be described using either one of the two titles: " A first course in numerical analysis " and " Advanced level programming of numerical methods with MATLAB ". As implied by the two titles, the book can be used as the textbook of an introductory numerical analysis course… (More)
The numerical investigation of a recent family of algebraic fractional-step methods for the solution of the incom-pressible time-dependent Navier–Stokes equations is presented. These methods are improved versions of the Yosida and one of them (the Yosida4 method) is proposed in this paper for the first time. They rely on an approximate LU block… (More)
We introduce some parallel domain decomposition preconditioners for iterative solution of sparse linear systems like those arising from the approximation of partial differential equations by finite elements or finite volumes. We first give an overview of algebraic domain decomposition techniques. We then introduce a preconditioner based on a multilevel… (More)
The numerical investigation of a recent family of algebraic fractional-step methods (the so called Yosida methods) for the solution of the incompressible time-dependent Navier–Stokes equations is presented. A comparison with the Karniadakis–Israeli–Orszag method Karniadakis et al. (1991, J. Comput. Phys. 97, 414–443) is carried out. The high accuracy in… (More)
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.
(!) indica un argomento fondamentale, (F) un argomento facoltativo, (*) un argo-mento o dimostrazione impegnativi, (NR) una dimostrazione non richiesta riferimento bibliografico: Differenze finite per ODEs e PDEs • (!) dato un problema ai valori iniziali y ′ = f (t, y), t ∈ [t 0 , t f ]; y(t 0) = y 0 , con f di classe C 1 tale che |∂f /∂y| ≤ L, si dimostri… (More)
A mixed nite element formulation for eeciently computing the velocity eld for uid ows in porous media is presented. Raviart Thomas (RT 0) and Brezzi Douglas Marini (BDM 1) spaces of lowest order are considered and compared both on analytic and realistic test cases. The BDM 1 space proves to be preferable to the simpler RT 0 with respect to CPU time and… (More)