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Finite Elements and Virtual Elements on Classical Meshes

Among Numerical Methods for PDEs, the Virtual Element Methods were introduced recently in order to allow the use of decompositions of the computational domain in polytopes (polygons or polyhedra) of very general shape. The present paper investigates the possible interest in their use&#x...

Least-squares formulations for eigenvalue problems associated with linear elasticity

We study the approximation of the spectrum of least-squares operators arising from linear elasticity. We consider a two-field (stress/displacement) and a three-field (stress/displacement/vorticity) formulation; other formulations might be analyzed with similar techniques. We prove a priori estimates&#...

An Adaptive Finite Element Scheme for the Hellinger-Reissner Elasticity Mixed Eigenvalue Problem

In this paper, we study the approximation of eigenvalues arising from the mixed Hellinger-Reissner elasticity problem by using a simple finite element introduced recently by one of the authors. We prove that the method converges when a residual type error estimator is considered an...

Convergence analysis of the scaled boundary finite element method for the Laplace equation

The scaled boundary finite element method (SBFEM) is a relatively recent boundary element method that allows the approximation of solutions to partial differential equations (PDEs) without the need of a fundamental solution. A theoretical framework for the convergence analysis of SBFEM is&#x...

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.

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Prodotti recenti

Finite Elements and Virtual Elements on Classical Meshes

Least-squares formulations for eigenvalue problems associated with linear elasticity

An Adaptive Finite Element Scheme for the Hellinger-Reissner Elasticity Mixed Eigenvalue Problem

Convergence analysis of the scaled boundary finite element method for the Laplace equation

On the existence and the uniqueness of the solution to a fluid-structure interaction problem

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