A Consistent Immersed Finite Element Method for the Interface Elasticity Problems - Sangwon Jin; Do Y. Kwak; Daehyeon Kyeong (Advances in Mathematical Physics)
We propose a new scheme for elasticity problems having discontinuity in the coefficients. In the previous work (Kwak et al., 2014), the authors suggested a method for solving such problems by finite element method using nonfitted grids. The proposed method is based on the P1-nonconforming finite element methods with stabilizing terms. In this work, we modify the method by adding the consistency terms, so that the estimates of consistency terms are not necessary. We show optimal error estimates in H1 and divergence norms under minimal assumptions. Various numerical experiments also show optimal rates of convergence.