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Some new analysis results for a class of interface problems
Author(s) -
Li Zhilin,
Wang Li,
Aspinwall Eric,
Cooper Racheal,
Kuberry Paul,
Sanders Ashley,
Zeng Ke
Publication year - 2015
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.2865
Subject(s) - classification of discontinuities , gravitational singularity , mathematics , singularity , dirac delta function , boundary value problem , jump , mathematical analysis , boundary (topology) , norm (philosophy) , differential equation , interface (matter) , function (biology) , computer science , physics , quantum mechanics , political science , law , bubble , maximum bubble pressure method , evolutionary biology , parallel computing , biology
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.