Some numerical techniques for solving elliptic interface problems

Many physical phenomena can be modeled by partial differential equations with singularities and interfaces. The standard finite difference and finite element methods may not be successful in giving satisfactory numerical results for such problems. Hence, many new methods have been developed. Some of them are developed with the modifications in the standard methods, so that they can deal with the discontinuities and the singularities. In this article, a survey has been done on some recent efficient techniques to solve elliptic interface problems. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 28: 94‐114, 2012