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Solving elliptic interface problems with jump conditions on Cartesian grids
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DOI：10.1016/j.jcp.2020.109269.png)
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Abstract
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We present a simple numerical algorithm for solving elliptic equations where the diffusion coefficient, the source term, the solution and its flux are discontinuous across an irregular interface. The algorithm produces second-order accurate solutions and first-order accurate gradients in the L-infinity-norm on Cartesian grids. The condition number is bounded, regardless of the ratio of the diffusion constant and scales like that of the standard 5-point stencil approximation on a rectangular grid with no interface. Numerical examples are given in two and three spatial dimensions. (C) 2020 Elsevier Inc. All rights reserved.
Keywords:
Poisson equation
Immersed interface
Level-set method
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