Publications related to Numerical Approximation of Flows in Random Porous Media

BPX-preconditioning for isogeometric analysis

We consider elliptic PDEs (partial differential equations) in the framework of isogeometric analysis, i.e., we treat the physical domain by means of a B-spline or NURBS mapping which we assume to be regular. The numerical solution of the PDE is computed by ...

2013

Optimal control for Partial Differential Equations

Antoine Giovanni Imboden

In this project report, we first present the application of the finite elements method to the numerical approximation of elliptic and parabolic PDEs over two-dimensional domains. We then consider the theory and numerical approximation of optimal control pr ...

2013

Stochastic Optimal Robin Boundary Control Problems of Advection-Dominated Elliptic Equations

Alfio Quarteroni, Gianluigi Rozza, Peng Chen

In this work we deal with a stochastic optimal Robin boundary control problem constrained by an advection-diffusion-reaction elliptic equation with advection-dominated term. We assume that the uncertainty comes from the advection led and consider a stochas ...

Society for Industrial and Applied Mathematics2013

Density approximations for multivariate affine jump-diffusion processes

Damir Filipovic

We introduce closed-form transition density expansions for multivariate affine jump-diffusion processes. The expansions rely on a general approximation theory which we develop in weighted Hilbert spaces for random variables which possess all polynomial mom ...

Elsevier2013

MATHICSE Technical Report : Analytic regularity and collocation approximation for PDEs with random domain deformations

Fabio Nobile

In this work we consider the problem of approximating the statistics of a given Quantity of Interest (QoI) that depends on the solution of a linear elliptic PDE defined over a random domain parameterized by N random variables. The elliptic problem is remap ...

MATHICSE2013

Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces

Fabio Nobile, Giovanni Migliorati, Erik Gustaf Bogislaw Von Schwerin

In this work we consider the random discrete

L^2

projection on polynomial spaces (hereafter RDP) for the approximation of scalar quantities of interest (QOIs) related to the solution of a partial differential equation model with random input parameters. ...

Siam Publications2013

MATHICSE Technical Report : Perturbation analysis for the Darcy problem with log-normal permeability

Fabio Nobile, Francesca Bonizzoni

We study the single-phase flow in a saturated, bounded heterogeneous porous medium. We model the permeability as a log-normal random field. We perform a perturbation analysis, expanding the solution in Taylor series. The series is directly computable in th ...

MATHICSE2013

Convergence of a stabilized discontinuous Galerkin method for incompressible nonlinear elasticity

Alfio Quarteroni, Ricardo Esteban Ruiz Baier, Davide Baroli

In this paper we present a discontinuous Galerkin method applied to incompressible nonlinear elastostatics in a total Lagrangian deformation-pressure formulation, for which a suitable interior penalty stabilization is applied. We prove that the proposed di ...

Springer Verlag2013

Computational Reduction for Parametrized PDEs: Strategies and Applications

Alfio Quarteroni, Gianluigi Rozza, Andrea Manzoni

In this paper we present a compact review on the mostly used techniques for computational reduction in numerical approximation of partial differential equations. We highlight the common features of these techniques and provide a detailed presentation of th ...

Springer Verlag2012

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

Numerical Approximation of Flows in Random Porous Media

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BPX-preconditioning for isogeometric analysis

Optimal control for Partial Differential Equations

Stochastic Optimal Robin Boundary Control Problems of Advection-Dominated Elliptic Equations

Density approximations for multivariate affine jump-diffusion processes

MATHICSE Technical Report : Analytic regularity and collocation approximation for PDEs with random domain deformations

Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces

MATHICSE Technical Report : Perturbation analysis for the Darcy problem with log-normal permeability

Convergence of a stabilized discontinuous Galerkin method for incompressible nonlinear elasticity

Computational Reduction for Parametrized PDEs: Strategies and Applications

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

Optimal control for Partial Differential Equations

MATHICSE Technical Report : Perturbation analysis for the Darcy problem with log-normal permeability

Stochastic Optimal Robin Boundary Control Problems of Advection-Dominated Elliptic Equations

MATHICSE Technical Report : Analytic regularity and collocation approximation for PDEs with random domain deformations

Density approximations for multivariate affine jump-diffusion processes

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

Computational Reduction for Parametrized PDEs: Strategies and Applications

Approximation of Quantities of Interest in Stochastic PDEs by the Random Discrete $L^2$ Projection on Polynomial Spaces

BPX-preconditioning for isogeometric analysis

Convergence of a stabilized discontinuous Galerkin method for incompressible nonlinear elasticity