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Simplified immersed interface methods for elliptic interface problems with straight interfaces

Authors

  • Xiufang Feng,

    1. School of Mathematics and Computer Sciences, Ningxia University, Yinchuan, China
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  • Zhilin Li

    Corresponding author
    1. Department of Mathematics and Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695
    • Department of Mathematics and Center for Research in Scientific Computation, North Carolina State University, Raleigh, NC 27695
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Abstract

In this article, we propose simplified immersed interface methods for elliptic partial/ordinary differential equations with discontinuous coefficients across interfaces that are few isolated points in 1D, and straight lines in 2D. For one-dimensional problems or two-dimensional problems with circular interfaces, we propose a conservative second-order finite difference scheme whose coefficient matrix is symmetric and definite. For two-dimensional problems with straight interfaces, we first propose a conservative first-order finite difference scheme, then use the Richardson extrapolation technique to get a second-order method. In both cases, the finite difference coefficients are almost the same as those for regular problems. Error analysis is given along with numerical example. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 28: 188–203, 2012

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