𝔖 Bobbio Scriptorium
✦   LIBER   ✦

A FEM–DtN formulation for a non-linear exterior problem in incompressible elasticity

✍ Scribed by Gabriel N. Gatica; Luis F. Gatica; Ernst P. Stephan

Publisher
John Wiley and Sons
Year
2002
Tongue
English
Weight
175 KB
Volume
26
Category
Article
ISSN
0170-4214

No coin nor oath required. For personal study only.

✦ Synopsis

Abstract

In this paper, we combine the usual finite element method with a Dirichlet‐to‐Neumann (DtN) mapping, derived in terms of an infinite Fourier series, to study the solvability and Galerkin approximations of an exterior transmission problem arising in non‐linear incompressible 2d‐elasticity. We show that the variational formulation can be written in a Stokes‐type mixed form with a linear constraint and a non‐linear main operator. Then, we provide the uniqueness of solution for the continuous and discrete formulations, and derive a Cea‐type estimate for the associated error. In particular, our error analysis considers the practical case in which the DtN mapping is approximated by the corresponding finite Fourier series. Finally, a reliable a posteriori error estimate, well suited for adaptive computations, is also given. Copyright © 2003 John Wiley & Sons, Ltd.

📜 SIMILAR VOLUMES

A mixed-FEM formulation for nonlinear in
A mixed-FEM formulation for nonlinear incompressible elasticity in the plane
✍ Gabriel N. Gatica; Ernst P. Stephan 📂 Article 📅 2001 🏛 John Wiley and Sons 🌐 English ⚖ 196 KB

## Abstract This article deals with an expanded mixed finite element formulation, based on the Hu‐Washizu principle, for a nonlinear incompressible material in the plane. We follow our related previous works and introduce both the stress and the strain tensors as further unknowns, which yields a tw

A transmission problem with non-linear i
A transmission problem with non-linear internal damping in elasticity
✍ Higidio Portillo Oquendo 📂 Article 📅 2003 🏛 John Wiley and Sons 🌐 English ⚖ 141 KB

## Abstract We consider an anisotropic body constituted by two different types of materials: a part is simple elastic while the other has a non‐linear internal damping. We show that the dissipation caused by the damped part is strong enough to produce uniform decay of the energy, more precisely, th

A Domain Decomposition Method Based on B
A Domain Decomposition Method Based on BEM and FEM for Linear Exterior Boundary Value Problems
✍ Gabriel N. Gatica; George C. Hsiao; Mario E. Mellado 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 137 KB

We develop the finite dimensional analysis of a new domain decomposition method for linear exterior boundary value problems arising in potential theory and heat conductivity. Our approach uses a Dirichlet-to-Neumann mapping to transform the exterior problem into an equivalent boundary value problem

A finite difference perturbation procedu
A finite difference perturbation procedure for non-linear elastic stability problems
✍ M. S. El Naschie; I. Galaly; S. Athel 📂 Article 📅 1978 🏛 John Wiley and Sons 🌐 English ⚖ 266 KB

A finite difference perturbation scheme is developed which allows a simple solution to a wide class of non-linear bifurcation problems. The analysis shows that in order to determine the initial post buckling behaviour accurately, it is not necessary to solve more than the linear eigenvalue differenc

A new stabilization technique for finite
A new stabilization technique for finite elements in non-linear elasticity
✍ S. Reese; M. Küssner; B. D. Reddy 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 495 KB 👁 2 views

In the present contribution, an innovative stabilization technique for two-dimensional low-order ÿnite elements is presented. The new approach results in an element formulation that is much simpler than the recently proposed enhanced strain element formulation, yet which gives results of at least th