We present a systematic description and comparison of the Finite Element Method (FEM) with relatively new Virtual (VEM) for solving boundary value problems in linear elasticity, including primal mixed formulations. The highlights common base essential difference between FEM VEM: discretisation same (Galerkin) weak formulations assembly element-wise quantities, but different approaches to elemen...

In this paper we investigate the regularization and numerical solution of geometric inverse problems related to linear elasticity with minimal assumptions on the geometry of the solution. In particular we consider the probably severely ill-posed reconstruction problem of a twodimensional inclusion from a single boundary measurement. In order to avoid parameterizations, which would introduce a-p...

The related physical equations of linear elasticity are the equilibrium equation and the constitutive equation, which expresses a relation between the stress and strain tensors. This is a first-order partial differential system such that a least squares method based on a stress-displacement formulation can be used whose corresponding finite element approximation does not preserve the symmetry o...

Abstract — In this paper, we present a non-conforming hp computational modeling methodology for solving elasticity problems. We consider the incompressible elasticity model formulated as a mixed displacement-pressure problem on a global domain which is partitioned into several local subdomains. The approximation within each local subdomain is designed using div-stable hp-mixed finite elements. ...

Enriched finite element approaches such as the extended finite element method provide a framework for constructing approximations to solutions of non-smooth problems. Internal features, such as boundaries, are represented in such methods by using discontinuous enrichment of the standard finite element basis. Within such frameworks, however, imposition of interface constraints and/or constitutiv...