Journal
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS
Volume 29, Issue 2, Pages 619-646Publisher
WILEY
DOI: 10.1002/num.21722
Keywords
immersed finite element; moving interface; Crank-Nicolson scheme; Cartesian mesh
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Funding
- NSF [DMS-1016313]
- GRF grant of Hong Kong [PolyU 501709]
- AMSS-PolyU Joint Research Institute for Engineering and Management of PolyU, NSERC (Canada)
- National Science Foundation of China [10875034]
- Direct For Mathematical & Physical Scien
- Division Of Mathematical Sciences [1016313] Funding Source: National Science Foundation
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This article presents three Crank-Nicolson-type immersed finite element (IFE) methods for solving parabolic equations whose diffusion coefficient is discontinuous across a time dependent interface. These methods can use a fixed mesh because IFEs can handle interface jump conditions without requiring the mesh to be aligned with the interface. These methods will be compared analytically in the sense of accuracy and computational cost. Numerical examples are provided to demonstrate features of these three IFE methods. (C) 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013
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