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Solving Elliptic Interface Problems with Jump Conditions on Cartesian Grids (1905.08718v2)

Published 21 May 2019 in physics.comp-ph, cs.NA, and math.NA

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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