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In this article we try to provide a review of recent works that propose numerical solutions of interface problems in the context of interpolation and approximation. We examine works that deal with adapted methods for polynomial interpolation and approximation, multiresolution and subdivision schemes, Hermite splines, approximation by B-splines, and some applications to numerical integration formulas. The discussion considers the applications, benefits, and potential challenges of these techniques when facing the solution of this kind of interface problems. This review is intended to serve as a reference for researchers who are interested in using these methods to approximate interface problems in this context.

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A Review of Numerical Methods Inspired by the Immersed Interface Method (IIM) for Solving Non-PDE Discontinuity Problems

  • 会议论文

  • 发表日期：

    2026年

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  • Juan Ruiz-Álvarez,
  • Dionisio F. Yáñez

摘要

In this article we try to provide a review of recent works that propose numerical solutions of interface problems in the context of interpolation and approximation. We examine works that deal with adapted methods for polynomial interpolation and approximation, multiresolution and subdivision schemes, Hermite splines, approximation by B-splines, and some applications to numerical integration formulas. The discussion considers the applications, benefits, and potential challenges of these techniques when facing the solution of this kind of interface problems. This review is intended to serve as a reference for researchers who are interested in using these methods to approximate interface problems in this context.