Approximation capabilities of immersed finite element spaces for elasticity Interface problems. Issue 3 (15th January 2019)

• Record Type: Journal Article
• Authors: Guo, Ruchi; Lin, Tao; Lin, Yanping
• Is Part Of: Numerical methods for partial differential equations. Volume 35:Issue 3(2019)
• Page Start: 1243
• Page End: 1268
• Publication Date: 2019-01-15
• Subjects: discontinuous coefficients -- elasticity equations -- immersed finite element method -- interface problems; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22348
• Languages: English
• ISSNs: 0749-159X

Abstract

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.