Karageorghis, A.; Sivaloganathan, S. Conforming spectral approximations for non-conforming domain decompositions. (English) Zbl 0943.65149 Comput. Methods Appl. Mech. Eng. 156, No. 1-4, 299-308 (1998). Summary: A spectral domain decomposition scheme is introduced for the numerical solution of second- and fourth-order elliptic problems. The technique is applicable to certain domain decompositions of rectangular or rectangularly decomposable domains. It is shown that it yields approximations which are pointwise \(C^0\) continuous across the subdomain interfaces for second-order problems and pointwise \(C^1\) continuous across the subdomain interfaces for fourth-order problems. Cited in 2 Documents MSC: 65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs 65N35 Spectral, collocation and related methods for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations 35J40 Boundary value problems for higher-order elliptic equations Keywords:Chebyshev polynomials; collocation; spectral domain decomposition; second- and fourth-order elliptic problems PDFBibTeX XMLCite \textit{A. Karageorghis} and \textit{S. Sivaloganathan}, Comput. Methods Appl. Mech. Eng. 156, No. 1--4, 299--308 (1998; Zbl 0943.65149) Full Text: DOI References: [1] Canuto, C.; Hussaini, M.; Quarteroni, A.; Zang, T., Spectral Methods in Fluid Dynamics (1988), Springer-Verlag: Springer-Verlag New York · Zbl 0658.76001 [2] Karageorghis, A., A fully conforming spectral collocation scheme for second and fourth order problems, Comput. Methods Appl. Mech. Engrg., 126, 305-314 (1995) · Zbl 0945.65522 [3] Belhachmi, Z.; Bernardi, C., Resolution of fourth-order problems by the mortar element method, Comput. Methods Appl. Mech. Eng., 116, 53-58 (1994) · Zbl 0824.65111 [4] Belhachmi, Z., Résolution de problèmes d’ordre quatre par la méthode des éléments a joints, Thèse Univ. Paris, VI (1994) [5] Boyd, J. P., Chebyshev and Fourier Spectral Method (1989), Springer-Verlag: Springer-Verlag Berlin [6] Karageorghis, A.; Phillips, T. N., Conforming Chebyshev spectral collocation methods for the solution of laminar flow in a constricted channel, IMA J. Numer. Anal., 11, 33-54 (1991) · Zbl 0709.76039 [7] Dennis, S. C.R.; Smith, F. T., Steady flow through a channel contraction with a symmetrical constriction in the form of a step, (Proc. Roy. Soc. Lond. A, 372 (1980)), 303-414 · Zbl 0455.76037 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.