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We study a recent formulation for fluid-structure interaction problems based on the use of a distributed Lagrange multiplier in the spirit of the fictitious domain approach. In this paper, we focus our attention on a crucial computational…
We study a recently introduced formulation for fluid-structure interaction problems which makes use of a distributed Lagrange multiplier in the spirit of the fictitious domain method. The time discretization of the problem leads to a mixed…
We consider a distributed Lagrange multiplier formulation for fluid-structure interaction problems in the spirit of the fictitious domain approach. This is an unfitted method, which does not require the construction of meshes conforming to…
We review the main features of an unfitted finite element method for interface and fluid-structure interaction problems based on a distributed Lagrange multiplier in the spirit of the fictitious domain approach. We recall our theoretical…
In this paper we describe a computational model for the simulation of fluid-structure interaction problems based on a fictitious domain approach. We summarize the results presented over the last years when our research evolved from the…
In this paper, new unfitted mixed finite elements are presented for elliptic interface problems with jump coefficients. Our model is based on a fictitious domain formulation with distributed Lagrange multiplier. The relevance of our…
Many physical problems involving heterogeneous spatial scales, such as the flow through fractured porous media, the study of fiber-reinforced materials, or the modeling of the small circulation in living tissues -- just to mention a few…
We study a finite element approximation of a coupled fluid-structure interaction consisting of a three-dimensional incompressible viscous fluid governed by the unsteady Stokes equations and a two-dimensional elastic plate. To avoid the use…
The aim of this work is to present a parallel solver for a formulation of fluid-structure interaction (FSI) problems which makes use of a distributed Lagrange multiplier in the spirit of the fictitious domain method. The fluid subproblem,…
This work focuses on the development of a non-conforming domain decomposition method for the approximation of PDEs based on weakly imposed transmission conditions: the continuity of the global solution is enforced by a discrete number of…
Simulations of fluid flow in naturally fractured rocks have implications for several subsurface applications, including energy storage and extraction, and waste storage. We are interested in flow in discrete fracture networks, which…
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…
The numerical approximation of incompressible fluid-structure interaction problems with Lagrange multiplier is generally based on strongly coupled schemes. This delivers unconditional stability but at the expense of solving a…
The flux-mortar mixed finite element method was recently developed for a general class of domain decomposition saddle point problems on non-matching grids. In this work we develop the method for Darcy flow using the multipoint flux…
This work presents a strongly coupled partitioned method for fluid-structure interaction (FSI) problems based on a monolithic formulation of the system which employs a Lagrange multiplier. We prove that both the semi-discrete and fully…
The implementation of the finite element method for linear elliptic equations requires to assemble the stiffness matrix and the load vector. In general, the entries of this matrix-vector system are not known explicitly but need to be…
The approximation properties of a quadratic iso-parametric finite element method for a typical cavitation problem in nonlinear elasticity are analyzed. More precisely, (1) the finite element interpolation errors are established in terms of…
We consider a recently introduced formulation for fluid-structure interaction problems which makes use of a distributed Lagrange multiplier in the spirit of the fictitious domain method. In this paper we focus on time integration methods of…
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…
Fluid flow in rough fractures and the coupling with the mechanical behaviour of the fractures pose great difficulties for numerical modeling approaches, due to complex fracture surface topographies, the non-linearity of hydromechanical…