The Brezzi–Pitkäranta stabilization scheme for the elasticity problem

Minghao Li ^[1] ; Dongyang Shi ^[2] ; Ying Dai ^[1]
1. [1] Tongji University
  
  Tongji University
  
  China
2. [2] Zhengzhou University
  
  Zhengzhou University
  
  China
Localización: Journal of computational and applied mathematics, ISSN 0377-0427, Vol. 286, Nº 1 (1 October 2015), 2015, págs. 7-16
Idioma: inglés
DOI: 10.1016/j.cam.2015.02.024
Enlaces
- Texto completo
Resumen
- In this paper, we consider the elasticity problem based on the Hellinger–Reissner variational principle. We use the equal order linear and bilinear mixed finite element spaces to approximate the stress and the displacement, and develop a Brezzi–Pitkäranta stabilization method for the finite element space pairs to overcome the lack of the inf–sup condition, then we give the error estimates of the stabilization approximation scheme. At last, we implement two numerical examples to test the stability and effectiveness of the proposed method.