College of Sciences
Mathematics and Statistics
Computational Applied Mathematics
Parabolic interface problems have many applications in physics and biology, such as hyperthermia treatment of cancer, underground water flow, and food engineering. Here we present an algorithm for solving two-dimensional parabolic interface problems where the coefficient and the forcing term have a discontinuity across the interface. The Crank-Nicolson scheme is used for time discretization, and the direct immersed interface method is used for spatial discretization. The proposed method is second order in both space and time for both solution and gradients in maximum norm.
Parabolic interface problems, Immersed interface method
Numerical Analysis and Computation | Partial Differential Equations
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Gamage, Kumudu and Peng, Yan, "A Spatially and Temporally Second Order Method for Solving Parabolic Interface Problems" (2022). College of Sciences Posters. 6.