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It is proved to be self-adjoint with compact resolvent on a simple Hilbert space. Its spectrum is characterized as being composed of a double set of eigenvalues: one converging towards $-\\infty$ and the other towards $+\\infty$, thus resulting in a nonsectorial operator. The decomposition of the convection-diffusion problem into a generalized eigenvalue problem permits the reduction of the original three-dimensional problem into a two-dimensional one. Despite the operator being nonsectorial, a complete solution on the infinite cylinder, associated to a step change of the wall temperature at the origin, is exhibited with the help of the operator's two sets of eigenvalues\/eigenfunctions. On the computational point of view, a mixed variational formulation is naturally associated to the eigenvalue problem. Numerical illustrations are provided for axisymmetrical situations, the convergence of which is found to be consistent with the numerical discretization.<\/jats:p>","DOI":"10.1137\/080736442","type":"journal-article","created":{"date-parts":[[2009,7,22]],"date-time":"2009-07-22T18:03:20Z","timestamp":1248285800000},"page":"658-676","source":"Crossref","is-referenced-by-count":15,"title":["Numerical Analysis of a New Mixed Formulation for Eigenvalue Convection-Diffusion Problems"],"prefix":"10.1137","volume":"70","author":[{"given":"C.","family":"Pierre","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"F.","family":"Plourabou\u00e9","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2009,7,22]]},"reference":[{"key":"R1","first-page":"55","volume":"14","author":"Aleksashenko V. A.","year":"1968","journal-title":"J. Engrg. Phys. 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