Spectral Solutions of Self-adjoint Elliptic Problems with Immersed Interfaces
Journal Article
·
· Applied Mathematics and Optimization
- University of Houston, Department of Mathematics (United States)
- Universite de Neuchatel, Institut de Mathematiques (Switzerland)
This paper describes a spectral representation of solutions of self-adjoint elliptic problems with immersed interfaces. The interface is assumed to be a simple non-self-intersecting closed curve that obeys some weak regularity conditions. The problem is decomposed into two problems, one with zero interface data and the other with zero exterior boundary data. The problem with zero interface data is solved by standard spectral methods. The problem with non-zero interface data is solved by introducing an interface space H{sub {Gamma}}({Omega}) and constructing an orthonormal basis of this space. This basis is constructed using a special class of orthogonal eigenfunctions analogously to the methods used for standard trace spaces by Auchmuty (SIAM J. Math. Anal. 38, 894-915, 2006). Analytical and numerical approximations of these eigenfunctions are described and some simulations are presented.
- OSTI ID:
- 22043842
- Journal Information:
- Applied Mathematics and Optimization, Journal Name: Applied Mathematics and Optimization Journal Issue: 3 Vol. 64; ISSN 0095-4616
- Country of Publication:
- United States
- Language:
- English
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