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arXiv · 1905.08718

Solving Elliptic Interface Problems with Jump Conditions on Cartesian Grids

Daniil Bochkov·Frederic Gibou
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Abstract

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 $L^\infty$-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.

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Daniil Bochkov, Frederic Gibou. 2019-05-21. Solving Elliptic Interface Problems with Jump Conditions on Cartesian Grids. https://doi.org/10.1016/j.jcp.2020.109269

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