A Nitsche extended finite element method for incompressible elasticity with discontinuous modulus of elasticity

✍ Scribed by Roland Becker; Erik Burman; Peter Hansbo

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 616 KB
• Volume: 198
• Category: Article
• ISSN: 0045-7825
• DOI: 10.1016/j.cma.2009.06.017

✦ Synopsis

Stokes' problem Discontinuous coefficients Surface tension a b s t r a c t

In this note we propose a finite element method for incompressible (or compressible) elasticity problems with discontinuous modulus of elasticity (or, if compressible, Poisson's ratio). The problem is written on mixed form using P 1 -continuous displacements and elementwise P 0 pressures, leading to the possibility of eliminating the pressure beforehand in the compressible case. In the incompressible case, the method is augmented by a stabilization term, penalizing the pressure jumps. We show a priori error estimates under certain regularity hypothesis. In particular we prove that if the exact solution is sufficiently smooth in each subdomain then the convergence order is optimal.