- Numerical solution of partial differential equations with random input data.
- A posteriori error estimation for finite
element approximation of elliptic problems, including discretization
error, modeling error and estimation of uncertainties.
-
Computational hemodynamics , fluid-structure interaction problems, Arbitrary Lagrangian Eulerian (ALE) formulation.
List of publications
- J. Bäck, F. Nobile, L. Tamellini, R. Tempone, Stochastic Galerkin and collocation methods for PDEs with random coefficients: a numerical comparison, ICES Report 09-33, submitted.
- L. Mirabella, F. Nobile, and A. Veneziani, An a posteriori error estimator for model adaptivity in electrocardiology, MOX-Report 27-2009, accepted for publication on Comp. Methods Appl. Mech. Engrg.
- L. Gerardo-Giorda, F. Nobile, and C. Vergara, Analysis and optimization of Robin-Robin partitioned procedures in fluid-structure interaction problems, MOX-Report 23-2009, submitted.
- F. Nobile and R. Tempone, Analysis and implementation issues for the numerical approximation of parabolic equations with random coefficients, Int. J. Numer. Methods Engrg, 2009, vol. 80/6-7, pp. 979-1006.
- S. Badia, F. Nobile and C. Vergara, Robin-Robin preconditioned Krylov methods for fluid-structure interaction problems, Comput. Methods Appl. Mech. Engrg., 2009, vol. 198/33-36, pp. 2768-2784.
- F. Nobile, Coupling strategies for the numerical simulation of blood flow in deformable arteries by 3D and 1D models, Mathematical and Computer Modelling, 2009, vol. 49/11-12, pp. 2152-2160.
- L. Gerardo-Giorda, L. Mirabella, F. Nobile, M. Perego and A. Veneziani, A model-based block-triangular preconditioner for the Bidomain system in electrocardiology, J. Comput. Physics, 2009, vol. 228/10, pp. 3625-3639.
- S. Badia, F. Nobile and C. Vergara, Fluid-structure partitioned procedures based on Robin transmission conditions , J. Comput. Physics, 2008, vol. 227/14, pp. 7027-7051.
- I. Babuska, F. Nobile and R. Tempone, Formulation of the static frame problem , Comput. Methods Appl. Mech. Engrg., 2008, vol. 197/29-32, pp. 2496-2499.
- I. Babuska, F. Nobile and R. Tempone, A systematic approach to model validation based on Bayesian updates and prediction related rejection criteria , Comput. Methods Appl. Mech. Engrg., 2008, vol. 197/29-32, pp. 2517-2539.
- F. Nobile, R. Tempone and C. Webster, An anisotropic sparse grid stochastic collocation method for partial differential equations with random input data , SIAM J. Numer. Anal., 2008, vol. 46/5, pp. 2411--2442.
- F. Nobile, R. Tempone and C. Webster
A sparse grid stochastic collocation method for partial differential equations with random input data , SIAM J. Numer. Anal., 2008, vol. 46/5, pp. 2309--2345.
- F. Nobile and C. Vergara, An effective fluid-structure interaction formulation for vascular dynamics by generalized Robin conditions , SIAM J. Sci. Comp., 2008, vol 30/2, pp. 731--763.
- I. Babuska, F. Nobile and R. Tempone, Reliability of Computational Science , Num. Methods for PDEs, 2007, vol. 23/4, pp. 753--784.
- L. Formaggia, A. Moura and F. Nobile, On the stability of the coupling of 3D and 1D fluid-structure interaction models for blood flow simulations , Math. Mod. Numer. Anal. (M2AN), 2007, vol. 41/4, pp. 743-769
- I. Babuska, F. Nobile and R. Tempone, A stochastic collocation method for elliptic partial differential equations with random input data, SIAM J. Num. Anal., 2007, vol. 45/3, pp. 1005--1034.
- I. Babuska, F. Nobile and R. Tempone, Worst-case scenario analysis for elliptic PDEs with uncertainty, Proceedings of the EURODYN conference, Paris, September 4-7, 2005.
- I. Babuska, F. Nobile and R. Tempone, Worst case scenario analysis for elliptic problems with uncertainty, Numer. Math. 101(2005), pp. 185--219.
- P. Causin, J-F. Gerbeau and F. Nobile,
Added-mass effect in the design of partitioned algorithms for
fluid-structure problems, Comput. Methods Appl. Mech. Engrg. 2005, vol. 194/42-44, pp. 4506--4527.
- J.T. Oden, I. Babuska, F. Nobile, Y. Feng and R. Tempone, Theory and methodology for estimation and control of errors due to modeling, approximation, and
uncertainty , Comput. Methods Appl. Mech. Engrg., 2005, vol. 194/2-5, pp. 195--204.
- L. Formaggia and F. Nobile,
Stability analysis of second order time accurate schemes for ALE-FEM, Comput. Methods Appl. Mech. Engrg., 193 (2004), pp. 4097-4116.
- S. Deparis, M.A. Fernández, L. Formaggia and F. Nobile,
Modified fixed point algorithm in fluid-structure
interaction, C.R. Mecanique, 2003, vol. 331, No. 8, pp. 525-530.
- F. Nobile,
A posteriori error estimates for the finite element approximation of
the Stokes problem, TICAM Report 03-13, April 2003, submitted.
- S. Prudhomme, F. Nobile, L. Chamoin and J.T. Oden, Analysis of a
subdomain-based error estimator for finite element approximations of
elliptic problems, Num. Methods for PDEs, vol 20/2,
pp. 165-192, 2003.
- L. Formaggia, F. Nobile, A. Quarteroni, A One Dimensional
Model for Blood Flow: Application to Vascular Prosthesis, in
Mathematical Modeling and Numerical Simulation in Continuum Mechanics, I.
Babuska, P.G. Ciarlet and T. Miyoshi eds., Lecture Notes in Computational Science and Engineering, vol 19, pp. 137-153, 2002, Springer-Verlag, Berlin.
- L. Formaggia, J.F. Gerbeau, F. Nobile, A. Quarteroni,
Numerical treatment of defective boundary conditions for the
Navier-Stokes equations, SIAM J. Numer. Anal., 2002, vol 40, No. 1, pp. 376-401 .
- L. Formaggia, F. Nobile, A. Quarteroni, A. Veneziani, P. Zunino,
Advances on numerical modelling of blood flow problems,Proceedings of ECCOMAS2000.
- L. Formaggia, J.F. Gerbeau,F. Nobile, A. Quarteroni,
On the Coupling of 3D and 1D Navier-Stokes equations for Flow Problems
in Compliant Vessels, Comput. Methods Appl. Mech. Engrg., vol.
191 (2001), pp. 561-582.
- L. Formaggia, F. Nobile, A. Quarteroni, A. Veneziani,
Multiscale Modelling of the Circulatory System: a Preliminary
Analysis, Comput. Visual. Sci 2 (1999) 2/3, 75-83.
- L. Formaggia and F. Nobile, A Stability Analysis for the
Arbitrary Lagrangian Eulerian Formulation with Finite Elements,
East-West Journal of Numerical Mathematics, vol. 7, 105-132, 1999.
- F. Nobile, A. Veneziani, Fluid Structure
Interaction in blood flow problems, ZAMM Z. Angew. Math. Mech. 79
(1999) S1, S255-S258 (Proceedings of the GAMM meeting 1998, Bremen).
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