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.
Original language | English |
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Pages (from-to) | 1243-1268 |
Number of pages | 26 |
Journal | Numerical Methods for Partial Differential Equations |
Volume | 35 |
Issue number | 3 |
DOIs | |
Publication status | Published - May 2019 |
Keywords
- discontinuous coefficients
- elasticity equations
- immersed finite element method
- interface problems
ASJC Scopus subject areas
- Analysis
- Numerical Analysis
- Computational Mathematics
- Applied Mathematics