Concept

Équation aux dérivées partielles elliptique

Publications associées (217)

MATHICSE Technical Report : Convergence of quasi-optimal stochastic Galerkin methods for a class of PDES with random coefficients

In this work we consider quasi-optimal versions of the Stochastic Galerkin Method for solving linear elliptic PDEs with stochastic coeffcients. In particular, we consider the case of a finite number N of random inputs and an analytic dependence of the solu ...

MATHICSE2012

On the optimal polynomial approximation of stochastic PDEs by Galerkin and Collocation methods

Fabio Nobile, Lorenzo Tamellini

In this work we focus on the numerical approximation of the solution u of a linear elliptic PDE with stochastic coefficients. The problem is rewritten as a parametric PDE and the functional dependence of the solution on the parameters is approximated by mu ...

World Scientific Publ Co Pte Ltd2012

Reduced Models for Optimal Control, Shape Optimization and Inverse Problems in Haemodynamics

Andrea Manzoni

The objective of this thesis is to develop reduced models for the numerical solution of optimal control, shape optimization and inverse problems. In all these cases suitable functionals of state variables have to be minimized. State variables are solutions ...

EPFL2012

Partitioned Solution of Geometrical Multiscale Problems for the Cardiovascular System

Adelmo Cristiano Innocenza Malossi

The aim of this work is the development of a geometrical multiscale framework for the simulation of the human cardiovascular system under either physiological or pathological conditions. More precisely, we devise numerical algorithms for the partitioned so ...

EPFL2012

An active strain electromechanical model for cardiac tissue

Alfio Quarteroni, Fabio Nobile, Ricardo Esteban Ruiz Baier

We propose a finite element approximation of a system of partial differential equations describing the coupling between the propagation of electrical potential and large deformations of the cardiac tissue. The underlying mathematical model is based on the ...

2012

Explicit methods for stiff stochastic differential equations

Assyr Abdulle

Multiscale differential equations arise in the modeling of many important problems in the science and engineering. Numerical solvers for such problems have been extensively studied in the deterministic case. Here, we discuss numerical methods for (mean-squ ...

Springer-Verlag Berlin2012

A stabilized finite volume element formulation for sedimentation-consolidation processes

Ricardo Esteban Ruiz Baier

A model of sedimentation-consolidation processes in so-called clarifier-thickener units is given by a parabolic equation describing the evolution of the local solids concentration coupled with a version of the Stokes system for an incompressible fluid desc ...

Siam Publications2012

On the efficiency of numerical homogenization methods

Assyr Abdulle

The subject of this workshop was numerical methods that preserve geometric properties of the flow of an ordinary or partial differential equation. This was complemented by the question as to how structure preservation affects the long-time behaviour of num ...

EMS2011

Multilevel Schwarz methods for elliptic partial differential equations

Alfio Quarteroni, Giovanni Migliorati

We investigate multilevel Schwarz domain decomposition preconditioners, to efficiently solve linear systems arising from numerical discretizations of elliptic partial differential equations by the finite element method. In our analysis we deal with unstruc ...

Elsevier2011

Link between Alginate Reaction Front Propagation and General Reaction Diffusion Theory

Jürgen Brugger, Philippe Renaud, Thomas Michael Braschler, Kristopher Pataky, Ana Valero, Ludovica Colella

We provide a common theoretical framework reuniting specific models for the Ca2+-alginate system and general reaction diffusion theory along with experimental validation on a microfluidic chip. As a starting point, we use a set of nonlinear, partial differ ...

2011

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