A mixed-FEM formulation for nonlinear incompressible elasticity in the plane

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

• Publisher: John Wiley and Sons
• Year: 2001
• Tongue: English
• Weight: 196 KB
• Volume: 18
• Category: Article
• ISSN: 0749-159X
• DOI: 10.1002/num.1046

✦ Synopsis

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 two‐fold saddle point operator equation as the corresponding variational formulation. A slight generalization of the classical Babuška‐Brezzi's theory is applied to prove unique solvability of the continuous and discrete formulations, and to derive the corresponding a priori error analysis. An extension of the well‐known PEERS space is used to define an stable associated Galerkin scheme. Finally, we provide an a posteriori error analysis based on the classical Bank‐Weiser approach. © 2002 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 18: 105–128, 2002