On a dimensional reduction method. I. The optimal selection of basis functions
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- by M. Vogelius and I. Babuška PDF
- Math. Comp. 37 (1981), 31-46 Request permission
Abstract:
This paper is the first in a series of three, which analyze an adaptive approximate approach for solving $(n + 1)$-dimensional boundary value problems by replacing them with systems of equations in n-dimensional space. In this approach the unknown functions of $(n + 1)$ variables are projected onto finite linear combinations of functions of just n variables. This paper shows how the coefficients of these linear combinations can be chosen optimally.References
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- M. Vogelius and I. Babuška, On a dimensional reduction method. I. The optimal selection of basis functions, Math. Comp. 37 (1981), no. 155, 31–46. MR 616358, DOI 10.1090/S0025-5718-1981-0616358-0 I. E. Zino & E. A. Tropp, Asymptotic Methods in the Problems of Heat Transfer and Thermoelasticity, Univ. of Leningrad Publ., Leningrad, 1978. (Russian)
Additional Information
- © Copyright 1981 American Mathematical Society
- Journal: Math. Comp. 37 (1981), 31-46
- MSC: Primary 65N99; Secondary 65J10
- DOI: https://doi.org/10.1090/S0025-5718-1981-0616358-0
- MathSciNet review: 616358