166 research outputs found
On the existence and the uniqueness of the solution to a fluid-structure interaction problem
In this paper we consider the linearized version of a system of partial
differential equations arising from a fluid-structure interaction model. We
prove the existence and the uniqueness of the solution under natural regularity
assumptions
Higher-order time-stepping schemes for fluid-structure interaction problems
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 second order based on backward differentiation formulae and on the
Crank-Nicolson method. We show the stability properties of the resulting
method; numerical tests confirm the theoretical results
Unfitted mixed finite element methods for elliptic interface problems
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
investigations is better seen when applied to the framework of fluid structure
interaction problems. Two finite elements schemes with piecewise constant
Lagrange multiplier are proposed and their stability is proved theoretically.
Numerical results compare the performance of those elements, confirming the
theoretical proofs and verifying that the schemes converge with optimal rate.Comment: 29 pages, 16 figures, 18 table
Immersed boundary method: performance analysis of popular finite element spaces
The aim of this paper is to understand the performances of different finite elements
in the space discretization of the Finite Element Immersed Boundary Method. In
this exploration we will analyze two popular solution spaces: Hood-Taylor and Bercovier-
Pironneau (P1-iso-P2). Immersed boundary solution is characterized by pressure discontinuities
at fluid structure interface. Due to such a discontinuity a natural enrichment
choice is to add piecewise constant functions to the pressure space. Results show that
P1 + P0 pressure spaces are a significant cure for the well known “boundary leakage”
affecting IBM. Convergence analysis is performed, showing how the discontinuity in the
pressure is affecting the convergence rate for our finite element approximation
Local enrichment of finite elements for interface problems
We consider interface problems for second order elliptic partial differential equations with Dirichlet boundary conditions. It is well known that the finite element discretization may fail to produce solutions converging with optimal rates unless the mesh fits with the discontinuity interface. We introduce a method based on piecewise linear finite elements on a non-fitting grid enriched with a local correction on a sub-grid constructed along the interface. We prove that our method recovers the optimal convergence rates both in H1 and in L2 depending on the local regularity of the solution. Several numerical experiments confirm the theoretical results
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