The Adaptive Immersed Interface Finite Element Method for Elasticity Interface Problems

Abstract

In this paper, we propose adaptive finite element methods with error control for solving elasticity problems with discontinuous coefficients. The meshes in the methods do not need to fit the interfaces. We establish a residual-based a posteriori error estimate which is $λ$-independent multiplicative constants; the Lamé constant $λ$ steers the incompressibility. The error estimators are then implemented and tested with promising numerical results which will show the competitive behavior of the adaptive algorithm.