Immersed finite element methods for parabolic equations with moving interface |
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| Authors: | Xiaoming He Tao Lin Yanping Lin Xu Zhang |
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| Institution: | 1. Department of Mathematics and Statistics, Missouri University of Science and Technology, Rolla, Missouri 65409;2. Department of Mathematics, Virginia Tech, Blacksburg, Virginia 24061;3. Department of Applied Mathematics, Hong Kong Polytechnic University, Hung Hom, Hong Kong;4. Department of Mathematical and Statistics Science, University of Alberta, Edmonton AB, Canada T6G 2G1 |
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| Abstract: | 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. © 2012 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2013 |
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| Keywords: | immersed finite element moving interface Crank‐Nicolson scheme Cartesian mesh |
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