Error estimates for the assumed stresses hybrid methods in the approximation of 4th order elliptic equations
La modellistica matematica e la fluidodinamica: una sintesi fra teoremi e mondo reale
Optimal control and numerical adaptivity for advection–diffusion equations
We propose a general approach for the numerical approximation of optimal control problems governed by a linear advection–diffusion equation, based on a stabilization method applied to the lagrangian functional, rather than stabilizing the state and adjoint equations separately. This approach yields a coherently stabilized control problem. Besides, it allows a straightforward a posteriori error estimate in which estimates of higher order terms are needless. Our a posteriori estimates stems from splitting...
Analysis of lumped parameter models for blood flow simulations and their relation with 1D models
This paper provides new results of consistence and convergence of the lumped parameters (ODE models) toward one-dimensional (hyperbolic or parabolic) models for blood flow. Indeed, lumped parameter models (exploiting the electric circuit analogy for the circulatory system) are shown to discretize continuous 1D models at first order in space. We derive the complete set of equations useful for the blood flow networks, new schemes for electric circuit analogy, the stability criteria that guarantee...
Simulazione numerica per la Coppa America di vela
Partendo dall’esperienza dell’École Polytechnique Fédérale di Lo- sanna (EPFL) quale consulente scientifico ufficiale del Team Alinghi, vincitore dell’edizione 2003 della Coppa America di vela, discutiamo il ruolo dei modelli matematici ed in particolare delle simulazioni numeriche basate sulla soluzione approssimata delle equazioni di Navier–Stokes mediate (Reynolds Averaged Navier-Stokes, RANS) e la loro integrazione nel ciclo di progetto. Risultati numerici in aree differenti (progetto di appendici,...
Navier-Stokes/Darcy coupling: modeling, analysis, and numerical approximation.
Optimal control and numerical adaptivity for advection–diffusion equations
We propose a general approach for the numerical approximation of optimal control problems governed by a linear advection–diffusion equation, based on a stabilization method applied to the Lagrangian functional, rather than stabilizing the state and adjoint equations separately. This approach yields a coherently stabilized control problem. Besides, it allows a straightforward error estimate in which estimates of higher order terms are needless. Our a posteriori estimates stems from splitting the error...
Analysis of lumped parameter models for blood flow simulations and their relation with 1D models
This paper provides new results of consistence and convergence of the lumped parameters (ODE models) toward one-dimensional (hyperbolic or parabolic) models for blood flow. Indeed, lumped parameter models (exploiting the electric circuit analogy for the circulatory system) are shown to discretize continuous 1D models at first order in space. We derive the complete set of equations useful for the blood flow networks, new schemes for electric circuit analogy, the stability criteria that...
A weighted empirical interpolation method: a priori convergence analysis and applications
We extend the classical empirical interpolation method [M. Barrault, Y. Maday, N.C. Nguyen and A.T. Patera, An empirical interpolation method: application to efficient reduced-basis discretization of partial differential equations. 339 (2004) 667–672] to a weighted empirical interpolation method in order to approximate nonlinear parametric functions with weighted parameters, random variables obeying various probability distributions. convergence analysis is provided for the proposed method and the...
Boundary control and shape optimization for the robust design of bypass anastomoses under uncertainty
We review the optimal design of an arterial bypass graft following either a (i) boundary optimal control approach, or a (ii) shape optimization formulation. The main focus is quantifying and treating the uncertainty in the residual flow when the hosting artery is not completely occluded, for which the worst-case in terms of recirculation effects is inferred to correspond to a strong orifice flow through near-complete occlusion.A worst-case optimal control approach is applied to the steady Navier-Stokes...
Generalized Reduced Basis Methods and n-width Estimates for the Approximation of the Solution Manifold of Parametric PDEs
The set of solutions of a parameter-dependent linear partial differential equation with smooth coefficients typically forms a compact manifold in a Hilbert space. In this paper we review the generalized reduced basis method as a fast computational tool for the uniform approximation of the solution manifold. We focus on operators showing an affine parametric dependence, expressed as a linear combination of parameter-independent operators through some smooth, parameter-dependent scalar functions....
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