2015 journal article

Some new analysis results for a class of interface problems

MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 38(18), 4530–4539.

By: Z. Li n, L. Wang*, E. Aspinwall*, R. Cooper*, P. Kuberry*, A. Sanders*, K. Zeng*

co-author countries: China 🇨🇳 United States of America 🇺🇸
author keywords: immersed boundary (IB) method; immersed interface method (IIM); jump conditions; discontinuous coefficient; Dirac delta function; weak solution; boundary singularity; convergence of IB method; equivalent boundary conditions
Source: Web Of Science
Added: August 6, 2018

Interface problems modeled by differential equations have many applications in mathematical biology, fluid mechanics, material sciences, and many other areas. Typically, interface problems are characterized by discontinuities in the coefficients and/or the Dirac delta function singularities in the source term. Because of these irregularities, solutions to the differential equations are not smooth or discontinuous. In this paper, some new results on the jump conditions of the solution across the interface are derived using the distribution theory and the theory of weak solutions. Some theoretical results on the boundary singularity in which the singular delta function is at the boundary are obtained. Finally, the proof of the convergency of the immersed boundary (IB) method is presented. The IB method is shown to be first‐order convergent in L ∞ norm. Copyright © 2013 John Wiley & Sons, Ltd.