1,720,981 research outputs found
Discrete Compactness Property for Quadrilateral Finite Element Spaces
No full textThe main purpose of the present article is to prove the discrete compactness property for Arnold-Boffi-Falk spaces of any order. Results of numerical experiments confirming the theory are also reported
A posteriori error estimates for an eigenvalue problem arising from fluid-structure interaction
No full textMixed approximation of eigenvalue problems : a superconvergence result
No full textWe state a superconvergence result for the lowest order Raviart-Thomas approximation of eigenvalue problems. It is known that a similar superconvergence result holds for the mixed approximation of Laplace problem; here we introduce a new proof, since the one given for the source problem cannot be generalized in a straightforward way to the eigenvalue problem. Numerical experiments confirm the superconvergence property and suggest that it also holds for the lowest order Brezzi-Douglas-Marini approximation
On a Superconvergence Result for Mixed Approximation of Eigenvalue Problems
No full textWe state a superconvergence result for the lowest order Raviart-Thomas approximation of eigenvalue problems. Numerical experiments confirm the superconvergence property and suggest that it holds also for the lowest order Brezzi-Douglas-Marini approximation
Local mass conservation of Stokes finite elements
No full textIn this paper we discuss the stability of some Stokes finite elements. In particular, we consider a modification of Hood–Taylor and Bercovier–Pironneau schemes which consists in adding piecewise constant functions to the pressure space. This enhancement, which had been already used in the literature, is driven by the goal of achieving an improved mass conservation at element level. The main result consists in proving the inf-sup condition for the enhanced spaces in a general setting and to present some numerical tests which confirm the stability properties. The improvement in the local mass conservation is shown in a forthcoming paper (Boffi et al. In: Papadrakakis, M., Onate, E., Schrefler, B. (eds.) Coupled Problems 2011. Computational Methods for Coupled Problems in Science and Engineering IV, Cimne, 2011) where the presented schemes are used for the solution of a fluid-structure interaction problem
Optimal convergence of adaptive FEM for eigenvalue clusters in mixed form
No full textIt 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
Mass Preserving Distributed Langrage Multiplier approach to Immersed Boundary Method
Full text linkThis research is devoted to mass conservation and CFL properties of the
Finite Elements Immersed Boundary Method. We first explore an enhanced higher order
scheme applied to the Finite Element Immersed Boundary Method technique introduced
by Boffi and Gastaldi. This technique is based on a Pointwise (PW) formulation of the
kinematic condition, and higher order elements show better conservation properties than
the original scheme. A further improvement with respect to the classical PW formulation
is achieved introducing a fully variational Distributed Lagrange Multiplier (DLM) formulation.
Numerical experiments show that DLM is not affected by any CFL condition.
Furthermore the mass conservation properties of this method are extremely competitive
A posteriori error analysis for nonconforming approximation of multiple eigenvalues
No full textIn this paper, we study an a posteriori error indicator introduced in E. Dari, R.G. Durán, and C. Padra, Appl. Numer. Math., 2012, for the approximation of the Laplace eigenvalue problem with Crouzeix–Raviart nonconforming 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
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