期刊
出版社
EDP SCIENCES S A
DOI: 10.1051/m2an/2016011
关键词
Immersed finite element method; Crouzeix-Raviart finite element; elasticity problems; heterogeneous materials; stability terms; Laplace-Young condition
资金
- NRF [2014R1A2A1A11053889]
- National Research Foundation of Korea [2014R1A2A1A11053889] Funding Source: Korea Institute of Science & Technology Information (KISTI), National Science & Technology Information Service (NTIS)
We develop a new finite element method for solving planar elasticity problems involving heterogeneous materials with a mesh not necessarily aligning with the interface of the materials. This method is based on the 'broken' Crouzeix-Raviart P-1-nonconforming finite element method for elliptic interface problems [D.Y. Kwak, K.T. Wee and K.S. Chang, SIAM J. Numer. Anal. 48 (2010) 2117-2134]. To ensure the coercivity of the bilinear form arising from using the nonconforming finite elements, we add stabilizing terms as in the discontinuous Galerkin (DG) method [D.N. Arnold, SIAM J. Numer. Anal. 19 (1982) 742-760, D.N. Arnold and F. Brezzi, in Discontinuous Galerkin Methods. Theory, Computation and Applications, edited by B. Cockburn, G.E. Karniadakis, and C.-W. Shu. Vol. 11 of Lecture Notes in Comput. Sci. Engrg. Springer-Verlag, NewYork (2000) 89-101, M.F. Wheeler, SIAM J. Numer. Anal. 15 (1978) 152-161.]. The novelty of our method is that we use meshes independent of the interface, so that the interface may cut through the elements. Instead, we modify the basis functions so that they satisfy the Laplace-Young condition along the interface of each element. We prove optimal H-1 and divergence norm error estimates. Numerical experiments are carried out to demonstrate that our method is optimal for various Lame parameters mu and lambda and locking free as lambda -> infinity.
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