Some new analysis results for a class of interface problems
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 s...
| Publié dans: | Mathematical methods in the applied sciences. - 1998. - 38(2015), 18 vom: 01. Dez., Seite 4530-4539 |
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| Auteur principal: | |
| Autres auteurs: | , , , , , |
| Format: | Article |
| Langue: | English |
| Publié: |
2015
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| Accès à la collection: | Mathematical methods in the applied sciences |
| Sujets: | Journal Article Dirac delta function Immersed Boundary (IB) method Immersed Interface Method (IIM) boundary singularity convergence of IB method discontinuous coefficient equivalent boundary conditions jump conditions weak solution |
| Résumé: | 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. Due to 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 method is presented. The IB method is shown to be first order convergent in L∞ norm |
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| Description: | Date Revised 01.10.2020 published: Print-Electronic Citation Status PubMed-not-MEDLINE |
| ISSN: | 0170-4214 |