Please use this identifier to cite or link to this item: http://hdl.handle.net/10397/87682
Title: Error estimates for a partially penalized immersed finite element method for elasticity interface problems
Authors: Guo, RC
Lin, T
Lin, YP 
Issue Date: 14-Jan-2020
Source: ESAIM : mathematical modelling and numerical analysis (ESAIM: M2AN), Jan. 2020, v. 54, no. 1, p. 1-24
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.
Keywords: Interface problems
Elasticity systems
Discontinuous Lame parameters
Immersed finite element methods
Publisher: EDP Sciences
Journal: ESAIM : mathematical modelling and numerical analysis (ESAIM: M2AN) 
ISSN: 0764-583X
EISSN: 1290-3841
DOI: 10.1051/m2an/2019051
Rights: © EDP Sciences, SMAI 2020
Posted with permission of the author.
The following publication Guo, R., Lin, T., & Lin, Y. (2020). Error estimates for a partially penalized immersed finite element method for elasticity interface problems. ESAIM: Mathematical Modelling and Numerical Analysis, 54(1), 1-24 is available at https://dx.doi.org/10.1051/m2an/2019051
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