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Introduction to dynamics with finite elements

Publications associées (35)

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Numerical Models for Differential Problems

Alfio Quarteroni

In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as w ...

Springer2009

Finite-element preconditioning of G-NI spectral methods

Alfio Quarteroni

Several old and new finite-element preconditioners for nodal-based spectral discretizations of −laplace(u) = f in the domain

\Omega = (-1, 1)^d

(d = 2 or 3), with Dirichlet or Neumann boundary conditions, are considered and compared in terms of bothcondi ...

2009

Multiscale algorithm with patches of finite elements

Jacques Rappaz, Marco Picasso, Vittoria Augusta Rezzonico Janka

We develop a discretization and solution technique for elliptic problems whose solutions may present strong variations, singularities, boundary layers and oscillations in localized regions. We start with a coarse finite element discretization with a mesh s ...

2008

Adaptive and Reduced Basis methods for optimal control problems in environmental applications

Luca Dede'

In this work we provide efficient numerical methods for the numerical solution of Partial Differential Equations (PDEs) and the computation of the associated outputs of interest, also in the frame of optimal control problems. With this aim, a goal-oriented ...

Politecnico di Milano2008

Kinetics of the Bose-Einstein condensation of microcavity polaritons - art. no. 689213

Vincenzo Savona, Davide Sarchi

We adopt a kinetic theory of polariton non-equilibrium Bose-Einstein condensation, to describe the formation of off-diagonal long-range order. The theory accounts properly for the dominant role of quantum fluctuations in the condensate. In realistic situat ...

SPIE-INT SOC OPTICAL ENGINEERING, PO BOX 10, BELLINGHAM, WA 98227-0010 USA2008

Multiscale algorithm with patches of finite elements and applications

Vittoria Augusta Rezzonico Janka

We develop a discretisation and solution technique for elliptic problems whose solutions may present strong variations, singularities, boundary layers and oscillations in localised regions. We start with a coarse finite element discretisation with a mesh s ...

EPFL2007

Long-range order in the Bose-Einstein condensation of polaritons

Vincenzo Savona, Davide Sarchi

We adopt a kinetic theory of polariton nonequilibrium Bose-Einstein condensation to describe the formation of off-diagonal long-range order. The theory accounts properly for the dominant role of quantum fluctuations in the condensate. In realistic situatio ...

2007

Finite element modelling and testing of an injection moulded generic tow reinforced structure

Martyn Douglas Wakeman

The deformation and fracture behaviour of a generic injection moulded structure reinforced by a robotically placed commingled glass fibre/polypropylene UD-tow (uni-directional) was simulated by finite elements. The suitability of modelling hybrid structure ...

2005

Iterative methods for Stokes/Darcy coupling

Marco Discacciati

We present iterative subdomain methods based on a domain decomposition approach to solve the coupled Stokes/Darcy problem using finite elements. The dependence of the convergence rate on the grid parameter h and on the physical data is discussed; some diff ...

2005

Approximation of multi-scale elliptic problems using patches of finite elements

Jacques Rappaz

In this paper we present a method to solve numerically elliptic problems with multi-scale data using multiple levels of not necessarily nested grids. The method consists in calculating successive corrections to the solution in patches whose discretizations ...

2003

Finite-element preconditioning of G-NI spectral methods

Alfio Quarteroni

Several old and new finite-element preconditioners for nodal-based spectral discretizations of −laplace(u) = f in the domain

\Omega = (-1, 1)^d

(d = 2 or 3), with Dirichlet or Neumann boundary conditions, are considered and compared in terms of bothcondi ...

2009