Stabilized mixed finite element methods for linear elasticity on simplicial grids in ℝn

19Citations
Citations of this article
9Readers
Mendeley users who have this article in their library.

Abstract

In this paper, we design two classes of stabilized mixed finite element methods for linear elasticity on simplicial grids. In the first class of elements, we use H (div , Ω S)-Pk and L2 (Ω ; ℝn)- Pk-1 to approximate the stress and displacement spaces, respectively, for 1 ≤ k ≤ n and employ a stabilization technique in terms of the jump of the discrete displacement over the edges/faces of the triangulation under consideration; in the second class of elements, we use H01 (Ω ; ℝn)- Pk to approximate the displacement space for 1 ≤ k ≤ n, and adopt the stabilization technique suggested by Brezzi, Fortin, and Marini [19]. We establish the discrete inf-sup conditions, and consequently present the a priori error analysis for them. The main ingredient for the analysis are two special interpolation operators, which can be constructed using a crucial H(div) bubble function space of polynomials on each element. The feature of these methods is the low number of global degrees of freedom in the lowest order case. We present some numerical results to demonstrate the theoretical estimates.

Cite

CITATION STYLE

APA

Chen, L., Hu, J., & Huang, X. (2017). Stabilized mixed finite element methods for linear elasticity on simplicial grids in ℝn. Computational Methods in Applied Mathematics, 17(1), 17–31. https://doi.org/10.1515/cmam-2016-0035

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free