Approximation capabilities of immersed finite element spaces for elasticity Interface problems. Issue 3 (15th January 2019) - Guo, Ruchi; Lin, Tao; Lin, Yanping
Abstract : We construct and analyze a group of immersed finite element (IFE) spaces formed by linear, bilinear, and rotated Q 1 polynomials for solving planar elasticity equation involving interface. The shape functions in these IFE spaces are constructed through a group of approximate jump conditions such that the unisolvence of the bilinear and rotated Q 1 IFE shape functions are always guaranteed regardless of the Lamé parameters and the interface location. The boundedness property and a group of identities of the proposed IFE shape functions are established. A multi‐point Taylor expansion is utilized to show the optimal approximation capabilities for the proposed IFE spaces through the Lagrange type interpolation operators.