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2003 AN OVERVIEW OF THE IMMERSED INTERFACE METHOD AND ITS APPLICATIONS
Zhilin Li
Taiwanese J. Math. 7(1): 1-49 (2003). DOI: 10.11650/twjm/1500407515

Abstract

Interface problems have many applications. Mathematically, interface problems usually lead to differential equations whose input data and solutions are non-smooth or discontinuous across some interfaces. The immersed interface method (IIM) has been developed in recent years particularly designed for interface problems. The IIM is a sharp interface method based on Cartesian grids. The IIM makes use of the jump conditions across the interface so that the finite difference/element discretization can be accurate. In this survey paper, we will introduce the immersed interface method for various problems, discuss its recent advances and related software packages, and some of its applications. We also review some other related methods and references in this survey paper.

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Zhilin Li. "AN OVERVIEW OF THE IMMERSED INTERFACE METHOD AND ITS APPLICATIONS." Taiwanese J. Math. 7 (1) 1 - 49, 2003. https://doi.org/10.11650/twjm/1500407515

Information

Published: 2003
First available in Project Euclid: 18 July 2017

zbMATH: 1028.65108
MathSciNet: MR1961037
Digital Object Identifier: 10.11650/twjm/1500407515

Subjects:
Primary: 65N06, 65N50

Rights: Copyright © 2003 The Mathematical Society of the Republic of China

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Vol.7 • No. 1 • 2003
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