16 Dicembre, 2002 16:00

A new subdomain-based error estimator for finite element approximations of elliptic problems.

Fabio Nobile, University of Texas at Austin

Aula Seminari MOX - 6° piano, Dip. di Matematica

abstract

abstract

In this talk we present a sub-domain residual error estimator for
finite element approximations of elliptic problems. It is obtained by
solving local problems on patches of elements in weighted spaces and
provides for an upper bound on the energy norm of the error when the
local problems are solved in sufficiently enriched discrete spaces. A
guaranteed lower bound on the error can also be derived by a simple
postprocess of the solutions to the local problems.
We will present several numerical tests and discuss the reliability and
performance of this estimator.
We will finally address the case of constrained elliptic problems, such
as the Stokes equations.

11 Dicembre, 2002 

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

A doubly nonlinear evolution equation arising in a crystal growth process

Nobuyuki Kenmochi, Università di Chiba, Giappone

In this talk we present a sub-domain residual error estimator for
finite element approximations of elliptic problems. It is obtained by
solving local problems on patches of elements in weighted spaces and
provides for an upper bound on the energy norm of the error when the
local problems are solved in sufficiently enriched discrete spaces. A
guaranteed lower bound on the error can also be derived by a simple
postprocess of the solutions to the local problems.
We will present several numerical tests and discuss the reliability and
performance of this estimator.
We will finally address the case of constrained elliptic problems, such
as the Stokes equations.

5 Dicembre, 2002 15:45

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

Tools di gestione software

Prof. L. Formaggia, MOX - Politecnico di Milano

Aula Seminari MOX

In this talk we present a sub-domain residual error estimator for
finite element approximations of elliptic problems. It is obtained by
solving local problems on patches of elements in weighted spaces and
provides for an upper bound on the energy norm of the error when the
local problems are solved in sufficiently enriched discrete spaces. A
guaranteed lower bound on the error can also be derived by a simple
postprocess of the solutions to the local problems.
We will present several numerical tests and discuss the reliability and
performance of this estimator.
We will finally address the case of constrained elliptic problems, such
as the Stokes equations.

18 Novembre, 2002 15:00

Sezione di Calcolo delle Variazioni ed Equazioni Differenziali

A shell model allowing folds

Sylvia Anicic, MOX

Aula Seminari MOX - 6° piano dip. di matematica

abstract

abstract

Starting from the Kirchhoff-Love model, we formulate a new thin shell model in linearized
elasticity which can be applied to folded shells.
The presence of a fold is solely characterized by an additonal
constraint in the variational space.
The strain energy contains a membrane-bending coupling term and a new bending strain tensor $ chi_{ alpha beta}(u)$ which measures the
infinitesimal variations of the principal curvatures of a surface.
We establish a uniqueness and existence result for shells whose midsurfaces are of class $ mathcal{G}^1$, which includes curvature discontinuities.
We give explicit relative error estimates, which are of order $h^2$, on the difference between the solution of our model and the solution of the Kirchhoff-Love shell model.

11 Novembre, 2002 17:00

Seminario Matematico e Fisico di Milano

Analisi Algebrica Computazionale

Daniele Struppa, George Mason University, VA, USA

Dipartimento di Matematica - Università degli Studi di Milano - Via Saldini 50 - Milano - Sala di Rappresentanza

Starting from the Kirchhoff-Love model, we formulate a new thin shell model in linearized
elasticity which can be applied to folded shells.
The presence of a fold is solely characterized by an additonal
constraint in the variational space.
The strain energy contains a membrane-bending coupling term and a new bending strain tensor $ chi_{ alpha beta}(u)$ which measures the
infinitesimal variations of the principal curvatures of a surface.
We establish a uniqueness and existence result for shells whose midsurfaces are of class $ mathcal{G}^1$, which includes curvature discontinuities.
We give explicit relative error estimates, which are of order $h^2$, on the difference between the solution of our model and the solution of the Kirchhoff-Love shell model.

18 Ottobre, 2002 17:00

Seminario Matematico e Fisico di Milano

Presentazione della nuova rivistaMilan Journal of Mathematics

David Kinderlehrer, Carnegie Mellon, Pittsburgh

Dipartimento di Matematica - Università degli Studi di Milano - Via Saldini 50 - Milano - Sala di Rappresentanza

Starting from the Kirchhoff-Love model, we formulate a new thin shell model in linearized
elasticity which can be applied to folded shells.
The presence of a fold is solely characterized by an additonal
constraint in the variational space.
The strain energy contains a membrane-bending coupling term and a new bending strain tensor $ chi_{ alpha beta}(u)$ which measures the
infinitesimal variations of the principal curvatures of a surface.
We establish a uniqueness and existence result for shells whose midsurfaces are of class $ mathcal{G}^1$, which includes curvature discontinuities.
We give explicit relative error estimates, which are of order $h^2$, on the difference between the solution of our model and the solution of the Kirchhoff-Love shell model.

18 Ottobre, 2002 17:00

Seminario Matematico e Fisico di Milano

Presentazione della nuova rivistaMilan Journal of Mathematics

Benoît Perthame, Ecôle Normale Supérieure, Paris

Dipartimento di Matematica - Università degli Studi di Milano - Via Saldini 50 - Milano - Sala di Rappresentanza

Starting from the Kirchhoff-Love model, we formulate a new thin shell model in linearized
elasticity which can be applied to folded shells.
The presence of a fold is solely characterized by an additonal
constraint in the variational space.
The strain energy contains a membrane-bending coupling term and a new bending strain tensor $ chi_{ alpha beta}(u)$ which measures the
infinitesimal variations of the principal curvatures of a surface.
We establish a uniqueness and existence result for shells whose midsurfaces are of class $ mathcal{G}^1$, which includes curvature discontinuities.
We give explicit relative error estimates, which are of order $h^2$, on the difference between the solution of our model and the solution of the Kirchhoff-Love shell model.

18 Ottobre, 2002 17:00

Seminario Matematico e Fisico di Milano

Presentazione della nuova rivistaMilan Journal of Mathematics

Andrew Sommese, Notre Dame University, USA

Dipartimento di Matematica - Università degli Studi di Milano - Via Saldini 50 - Milano - Sala di Rappresentanza

Starting from the Kirchhoff-Love model, we formulate a new thin shell model in linearized
elasticity which can be applied to folded shells.
The presence of a fold is solely characterized by an additonal
constraint in the variational space.
The strain energy contains a membrane-bending coupling term and a new bending strain tensor $ chi_{ alpha beta}(u)$ which measures the
infinitesimal variations of the principal curvatures of a surface.
We establish a uniqueness and existence result for shells whose midsurfaces are of class $ mathcal{G}^1$, which includes curvature discontinuities.
We give explicit relative error estimates, which are of order $h^2$, on the difference between the solution of our model and the solution of the Kirchhoff-Love shell model.

18 Ottobre, 2002 17:00

Seminario Matematico e Fisico di Milano

Presentazione della nuova rivistaMilan Journal of Mathematics

Karl Strambach, Universität Erlangen

Dipartimento di Matematica - Università degli Studi di Milano - Via Saldini 50 - Milano - Sala di Rappresentanza

Starting from the Kirchhoff-Love model, we formulate a new thin shell model in linearized
elasticity which can be applied to folded shells.
The presence of a fold is solely characterized by an additonal
constraint in the variational space.
The strain energy contains a membrane-bending coupling term and a new bending strain tensor $ chi_{ alpha beta}(u)$ which measures the
infinitesimal variations of the principal curvatures of a surface.
We establish a uniqueness and existence result for shells whose midsurfaces are of class $ mathcal{G}^1$, which includes curvature discontinuities.
We give explicit relative error estimates, which are of order $h^2$, on the difference between the solution of our model and the solution of the Kirchhoff-Love shell model.

10 Ottobre, 2002 14:30

Seminario Matematico e Fisico di Milano

Classical and quantum semiconductor device modeling and simulation

prof. Ansgar Jungel, Universitaet Mainz, Germany

Aula Seminari MOX - Dip. mat.

abstract

abstract

The numerical simulation of modern semiconductor devices, like deep
submicron transistors or tunneling diodes, using microscopic models is
usually costly and time consuming. In recent years, fluiddynamical models
are derived, which contain the main physical phenomena and which can be
solved efficiently.

In this talk, a model hierarchy of classical and quantum fluid equations
for semiconductor devices is introduced and two models of this hierarchy
are discussed in detail: the quantum drift-diffusion equations and
the energy-transport models. A positivity-preserving numerical scheme
for the quantum drift-diffusion model is derived and numerical convergence
is proved. A simple 1D resonant tunneling diode is simulated showing
the expected physical behavior. Moreover, the classical energy-transport
equations are discretized using adaptively refined mixed finite elements
and a 2D MOSFET is numerically simulated.