caa a22 4500 445842091 CHVBK 20180317145347.0 cr unu---uuuuu 170323e20111201xx s 000 0 eng 10.1007/s00245-011-9142-0 doi (NATIONALLICENCE)springer-10.1007/s00245-011-9142-0 Spectral Solutions of Self-adjoint Elliptic Problems with Immersed Interfaces [Elektronische Daten] [G. Auchmuty, P. Klouček] 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 Γ(Ω) 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. Springer Science+Business Media, LLC, 2011 Immersed interface nationallicence Interface eigenproblem nationallicence Interface trace space nationallicence Auchmuty G. Department of Mathematics, University of Houston, 77204-3008, Houston, TX, USA aut Klouček P. Institut de Mathèmatiques, Universitè de Neuchâtel, Rue Emile Argand 11, 2007, Neuchâtel, Switzerland aut Applied Mathematics & Optimization Springer-Verlag 64/3(2011-12-01), 313-338 0095-4616 64:3<313 2011 64 245 https://doi.org/10.1007/s00245-011-9142-0 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00245-011-9142-0 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Auchmuty G. Department of Mathematics, University of Houston, 77204-3008, Houston, TX, USA aut NATIONALLICENCE 700 1- Klouček P. Institut de Mathèmatiques, Universitè de Neuchâtel, Rue Emile Argand 11, 2007, Neuchâtel, Switzerland aut NATIONALLICENCE 773 0- Applied Mathematics & Optimization Springer-Verlag 64/3(2011-12-01), 313-338 0095-4616 64:3<313 2011 64 245 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer