A RTk−Pk approximation for linear elasticity yielding a broken H(div) convergent postprocessed stress. (November 2015)

• Record Type: Journal Article
• Authors: Gatica, Gabriel N.; Gatica, Luis F.; Sequeira, Filánder A.
• Is Part Of: Applied mathematics letters. Volume 49(2015:Nov.)
• Page Start: 133
• Page End: 140
• Publication Date: 2015-11
• Subjects: Pseudostress–displacement formulation -- Linear elasticity -- Mixed finite element method -- 3D high-order approximations; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2015.05.009
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: We present a non-standard mixed finite element method for the linear elasticity problem in R n with non-homogeneous Dirichlet boundary conditions. More precisely, our approach is based on a simplified interpretation of the pseudostress–displacement formulation originally proposed in Arnold and Falk (1988), which does not require symmetric tensor spaces in the finite element discretization. We apply the classical Babuška–Brezzi theory to prove that the corresponding continuous and discrete schemes are well-posed. In particular, Raviart–Thomas spaces of order k ≥ 0 for the pseudostress and piecewise polynomials of degree ≤ k for the displacement can be utilized. In addition, complementing the results in the aforementioned reference, we introduce a new postprocessing formula for the stress recovering the optimally convergent approximation of the broken H ( div ) -norm. Numerical results confirm our theoretical findings.