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Spectral element method for three dimensional elliptic problems with smooth interfaces
Khan A., Husain A., Mohapatra S.,
Published in Elsevier B.V.
Volume: 315
Pages: 522 - 549
In this paper we propose a least-squares spectral element method for three dimensional elliptic interface problems. The differentiability estimates and the main stability theorem, using non-conforming spectral element functions, are proven. The proposed method is free from any kind of first order reformulation. A suitable preconditioner is constructed with help of the regularity estimate and proposed stability estimates which is used to control the condition number. We show that these preconditioners are spectrally equivalent to the quadratic forms by which we approximate them. We obtain the error estimates which show the exponential accuracy of the method. Numerical results are obtained for both straight and curved interfaces to show the efficiency of the proposed method. © 2016 Elsevier B.V.
About the journal
JournalData powered by TypesetComputer Methods in Applied Mechanics and Engineering
PublisherData powered by TypesetElsevier B.V.
Open AccessNo