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Lucia Gastaldi

Publications and source records attributed to Lucia Gastaldi.

27 records · Page 2Linked to original sources
arXiv2019

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.

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arXiv2018

Adaptive finite element method for the Maxwell eigenvalue problem

In this paper we prove the optimal convergence of a standard adaptive scheme based on edge finite elements for the approximation of the solutions of the eigenvalue problem associated with Maxwell's equations. The proof uses the known equivalence of the problem of interest with a mixed eigenvalue problem.

math.NA↗
arXiv2017

A distributed Lagrange formulation of the Finite Element Immersed Boundary Method for fluids interacting with compressible solids

We present a distributed Lagrange multiplier formulation of the Finite Element Immersed Boundary Method to couple incompressible fluids with compressible solids. This is a generalization of the formulation presented in Heltai and Costanzo (2012), that offers a cleaner variational formulation, thanks to the introduction of distributed Lagrange multipliers, that acts as intermediary between the fluid and solid equations, keeping the two formulation mostly separated. Stability estimates and a brief numerical validation are presented.

math.NA↗
arXiv2017

A fictitious domain approach with distributed Lagrange multiplier for fluid-structure interactions

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 problem for which a rigorous stability analysis is provided. The finite element space discretization is discussed and optimal convergence estimates are proved.

math.NA↗
arXiv2016

Residual-based a posteriori error estimation for the Maxwell's eigenvalue problem

We present an a posteriori estimator of the error in the L^2-norm for the numerical approximation of the Maxwell's eigenvalue problem by means of Nédélec finite elements. Our analysis is based on a Helmholtz decomposition of the error and on a superconvergence result between the L^2-orthogonal projection of the exact eigenfunction onto the curl of the Nédélec finite element space and the eigenfunction approximation. Reliability of the a posteriori error estimator is proved up to higher order terms and local efficiency of the error indicators is shown by using a standard bubble functions technique. The behavior of the a posteriori error estimator is illustrated on a numerical test.

math.NA↗
arXiv2015

Optimal convergence of adaptive FEM for eigenvalue clusters in mixed form

It is shown that the h-adaptive mixed finite element method for the discretization of eigenvalue clusters of the Laplace operator produces optimal convergence rates in terms of nonlinear approximation classes. The results are valid for the typical mixed spaces of Raviart-Thomas or Brezzi-Douglas-Marini type with arbitrary fixed polynomial degree in two and three space dimensions.

math.NA↗
arXiv2014

A posteriori error analysis for nonconforming approximation of multiple eigenvalues

In this paper we study an a posteriori error indicator introduced in E. Dari, R.G. Duran, C. Padra, Appl. Numer. Math., 2012, for the approximation of the Laplace eigenvalue problem with Crouzeix-Raviart non-conforming finite elements. In particular, we show that the estimator is robust also in presence of eigenvalues of multiplicity greater than one. Some numerical examples confirm the theory and illustrate the convergence of an adaptive algorithm when dealing with multiple eigenvalues.

math.NA↗
arXiv2014

Discrete models for fluid-structure interactions: the Finite Element Immersed Boundary Method

The aim of this paper is to provide a survey of the state of the art in the finite element approach to the Immersed Boundary Method (FE-IBM) which has been investigated by the authors during the last decade. In a unified setting, we present the different formulation proposed in our research and highlight the advantages of the one based on a distributed Lagrange multiplier (DLM-IBM) over the original FE-IBM.

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