Reference : A staggered cell-centered finite element method for compressible and nearly-incompres...
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A staggered cell-centered finite element method for compressible and nearly-incompressible linear elasticity on general meshes
Ong, Thanh Hai [> >]
Hoang, Thi Thao Phuong [> >]
Bordas, Stéphane mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Engineering Research Unit]
Nguyen-Xuan, H. [> >]
SIAM Journal on Numerical Analysis
[en] linear elasticity ; finite elements ; cell-centered schemes ; macroelement condition ; stability condition
[en] We propose a new numerical method, namely, the staggered cell-centered finite element method for compressible and nearly incompressible linear elasticity problems. By building a dual mesh and its triangular submesh, the scheme can be constructed from a general mesh in which the displacement is approximated by piecewise linear (P1) functions on the dual submesh and, in the case of nearly incompressible problems, the pressure is approximated by piecewise constant (P0) functions on the dual mesh. The scheme is cell centered in the sense that the solution can be computed by cell unknowns of the primal mesh (for the displacement) and of the dual mesh (for the pressure). The method is presented within a rigorous theoretical framework to show stability and convergence. In particular, for the nearly incompressible case, stability is proved by using the macroelement technique. Numerical results show that the method, compared with other methods, is effective in terms of accuracy and computational cost.

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