Abstract
This article is about the error analysis for a partially penalized immersed finite element (PPIFE) method designed to solve linear planar-elasticity problems whose Lamé parameters are piecewise constants with an interface-independent mesh. The bilinear form in this method contains penalties to handle the discontinuity in the global immersed finite element (IFE) functions across interface edges. We establish a stress trace inequality for IFE functions on interface elements, we employ a patch idea to derive an optimal error bound for the stress of the IFE interpolation on interface edges, and we design a suitable energy norm by which the bilinear form in this PPIFE method is coercive. These key ingredients enable us to prove that this PPIFE method converges optimally in both an energy norm and the usual L2 norm under the standard piecewise H2-regularity assumption for the exact solution. Features of the proposed PPIFE method are demonstrated with numerical examples.
Original language | English |
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Pages (from-to) | 1-24 |
Number of pages | 24 |
Journal | ESAIM: Mathematical Modelling and Numerical Analysis |
Volume | 54 |
Issue number | 1 |
DOIs | |
Publication status | Published - 14 Jan 2020 |
Keywords
- Discontinuous Lamé parameters
- Elasticity systems
- Immersed finite element methods
- Interface problems
ASJC Scopus subject areas
- Analysis
- Numerical Analysis
- Modelling and Simulation
- Computational Mathematics
- Applied Mathematics