### Seminari

### Prossimi Seminari

**Computational Prediction of Blood Damage**

Marek Behr, Chair for Computational Analysis of Technical Systems Faculty of Mechanical Engineering, RWTH Aachen

lunedì 1 ottobre 2018 alle ore 14:00, Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO**Caputo Evolution Equations with time-nonlocal initial condition**

Lorenzo Toniazzi, University of Warwick

martedì 9 ottobre 2018 alle ore 15:15, Aula Seminari 3° piano**Statistical modeling and monitoring of product and process quality in Additive Manufacturing: opportunities and challenges**

Bianca Maria Colosimo, Dipartimento di Meccanica, Politecnico di Milano

giovedì 11 ottobre 2018 alle ore 14:00, Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO**Elastic waves in soft tissues: inverse analysis, experiments, simulations, validation**

Michel Destrade, Chair of Applied Mathematics at NUI Galway

giovedì 18 ottobre 2018 alle ore 14:00, Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO**An overview of some mathematical and computational problems in Network Science**

Michele Benzi, Scuola Normale Superiore, Pisa

giovedì 22 novembre 2018 alle ore 14:00, Aula Consiglio VII Piano – Edificio 14, Dipartimento di Matematica POLITECNICO DI MILANO**BIRATIONAL EQUIVALENCE OF ALGEBRAIC VARIETIES**

Shigefumi Mori, Kyoto University Institute of Advanced Study

lunedì 26 novembre 2018 alle ore 16:30, Aula Chisini, Diparimento di Matematica, Via C. Saldini 50

### Seminari Passati

**Probabilistic representation of solution to nonlinear parabolic equations**

Francois Delarue, Universita di Parigi

domenica 9 febbraio 2003 alle ore 15:00, Dipartimento di Matematica**Parabolic differential-algebraic multiphysics models in electrical network design**

Giuseppe Alì, Ist. per le appl. del calcolo M. Picone – Napo

mercoledì 29 gennaio 2003 alle ore 11:30, Aula semianri MOX – 6° piano dip. mat.ABSTRACTIn refined network analysis, a compact network model is combined with distributed models for semiconductor devices in a multiphysics approach. For linear RLC networks containing diodes as distributed devices, we construct a mathematical model that combines the differential-algebraic network equations of the circuit with parabolic-elliptic boundary value problems modelling the diodes.

For this mixed initial-boundary value problem of partial differential-algebraic equations a first existence result is given.**Frattali**

S. Mortola, Dip. di Matematica

venerdì 17 gennaio 2003 alle ore 12:30, aula B 5.4**Problemi di controllo ottimo in economia**

Fausto Gozzi, LUISS – Roma

lunedì 13 gennaio 2003 alle ore 15:00, Dipartimento di Matematica**Buchi neri e singolarità nude**

G. Magli, Dip. di Matematica

venerdì 10 gennaio 2003 alle ore 12:30, aula B 5.4**Reconstruction and classification of distal anastomoses of peripheral by-pass grafts: from Magnetic Resonance Imaging to CFD**

Sergio Giordana, Imperial College – London

mercoledì 8 gennaio 2003 alle ore 15:00, Aula Seminari MOX – 6° piano – Dip. MatematicaABSTRACTAbnormal haemodynamic conditions are implicated in the development of anastomotic myointimal hyperplasia (MIH), which constitutes the main cause of failure of peripheral by-pass grafts. However these conditions are difficult to determine in-vivo, prompting research using ex-vivo idealised models. To relate the understanding gained in idealised geometries to anatomically correct conditions we have investigated an approach to classify in-vivo distal graft anastomoses and their inter-patient variability.

In-vivo distal anastomotic geometries were acquired by magnetic resonance (MR) angiography from 13 patients who had undergone infrageniculate autologous venous bypass surgery. On average, the images were acquired 2 weeks post-operatively. Five patients also underwent repeat examinations 2 to 7 weeks later. For each geometry, the surface of the arterial lumen is reconstructed from MR images using a zero level set of an implicit function constructed from radial basis functions that can be shown to minimise curvature. The final surface representation is a tessellation obtained by the marching cubes algorithm and is the initial support for CFD mesh generation.

The three-dimensional binary image created from the interpolated surface is processed using a skeletonisation algorithm to obtain the centreline of each branch in the geometry. This allows the definition and the computation of the set of parameters that constitute the base of a geometric classification. In this study we have chosen to measure the branching angles between straight line approximations of the centrelines obtained by averaging over a characteristic length of the anastomosis.

**Some Remarks on the History and Future of Averaging Techniques in A~Posteriori Finite Element Error Analysis**

Carsten Carstensen, Vienna University of Technology

martedì 7 gennaio 2003 alle ore 15:00, Aula Seminari MOX – 6° piano dipartimento di MatemABSTRACTGiven a flux or stress approximation $p_h$ from a low-order finite

element simulation of an elliptic boundary value problem, averaging or

(gradient-) recovery techniques aim the computation of an improved

approximation $Ap_h$ by a (simple) post processing of

$p_h$. For instance, frequently named after Zienkiewicz and Zhu,

$Ap_h$ is the elementwise interpolation of the nodal values

$(Ap_h)(z)$ obtained as the integral mean of $p_h$ on a

neighbourhood of $z$. This paper gives an

overview over old and new arguments in the proof of reliability and

efficiency of the error estimator $ eta_{ cal A}:= |p_h-{A}p_h |$

as an approximation of the error $ |p-p_h |$ in (an energy norm)

$ | cdot |$. High-lighted are the general class of meshes, averaging

operators, or finite elements [conforming, nonconforming, or mixed].

Emphasis is on old and new aspects of superconvergence and arguments

to circumvent superconvergence at all within proofs of a~posteriori

finite element error estimates.

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

Fabio Nobile, University of Texas at Austin

lunedì 16 dicembre 2002 alle ore 16:00, Aula Seminari MOX – 6° piano, Dip. di MatematicaABSTRACTIn 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.