Journal
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
Volume 28, Issue 1, Pages 312-330Publisher
WILEY
DOI: 10.1002/num.20620
Keywords
error estimates; finite element; immersed interface; interface problems
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Funding
- NSF [DMS-0713763]
- Research Grants Council of the Hong Kong Special Administrative Region, China [PolyU 501709]
- AMSS-PolyU Joint Research Institute for Engineering and Management Mathematics
- NSERC (Canada)
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This article analyzes the error in both the bilinear and linear immersed finite element (IFE) solutions for second-order elliptic boundary problems with discontinuous coefficients. The discontinuity in the coefficients is supposed to happen across general curves, but the mesh of the IFE methods can be allowed not to align with the curve of discontinuity. It has been shown that the bilinear and linear IFE solutions converge to the exact solution under the usual assumptions about the meshes and regularity. (C) 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 312-330, 2012
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