Zobrazeno 1 - 10
of 52
pro vyhledávání: '"Fournié, Michel"'
We use moment-SOS (Sum Of Squares) relaxations to address the optimal control problem of the 1D heat equation perturbed with a nonlinear term. We extend the current framework of moment-based optimal control of PDEs to consider a quadratic cost on the
Externí odkaz:
http://arxiv.org/abs/2411.11528
Autor:
Fournié, Michel, Lozinski, Alexei
We study a fictitious domain approach with Lagrange multipliers to discretize Stokes equations on a mesh that does not fit the boundaries. A mixed finite element method is used for fluid flow. Several stabilization terms are added to improve the appr
Externí odkaz:
http://arxiv.org/abs/1710.07935
Publikováno v:
Spectral and High Order Methods for Partial Differential Equations - ICOSAHOM'12, M. Azaiez et al. (eds.), pp. 217-226, Lecture Notes in Computational Science and Engineering 95, Springer, Berlin, Heidelberg, 2013
We present new high-order Alternating Direction Implicit (ADI) schemes for the numerical solution of initial-boundary value problems for convection-diffusion equations with mixed derivative terms. Our approach is based on the unconditionally stable A
Externí odkaz:
http://arxiv.org/abs/1505.07621
Autor:
Court, Sébastien, Fournié, Michel
The paper extends a stabilized fictitious domain finite element method initially developed for the Stokes problem to the incompressible Navier-Stokes equations coupled with a moving solid. This method presents the advantage to predict an optimal appr
Externí odkaz:
http://arxiv.org/abs/1502.03953
Autor:
Düring, Bertram, Fournié, Michel
Publikováno v:
J. Comput. Appl. Math. 236(17) (2012), 4462-4473
We derive a new high-order compact finite difference scheme for option pricing in stochastic volatility models. The scheme is fourth-order accurate in space and second-order accurate in time. Under some restrictions, theoretical results like uncondit
Externí odkaz:
http://arxiv.org/abs/1404.5140
Publikováno v:
J. Comput. Appl. Math. 271 (2014), 247-266
We derive high-order compact finite difference schemes for option pricing in stochastic volatility models on non-uniform grids. The schemes are fourth-order accurate in space and second-order accurate in time for vanishing correlation. In our numeric
Externí odkaz:
http://arxiv.org/abs/1404.5138
In this work we develop a fictitious domain method for the Stokes problem which allows computations in domains whose boundaries do not depend on the mesh. The method is based on the ideas of Xfem and has been first introduced for the Poisson problem.
Externí odkaz:
http://arxiv.org/abs/1401.0559
In the present work, we propose to extend to the Stokes problem a fictitious domain approach inspired by eXtended Finite Element Method and studied for Poisson problem in [Renard]. The method allows computations in domains whose boundaries do not mat
Externí odkaz:
http://arxiv.org/abs/1303.6850
Autor:
Fournié, Michel *, Morrison, Jonathan **
Publikováno v:
In IFAC PapersOnLine July 2017 50(1):12301-12306
Publikováno v:
IFAC-PapersOnLine; January 2024, Vol. 58 Issue: 6 p119-124, 6p