Publication:
Sobolev orthogonal polynomials on product domains

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URI: http://hdl.handle.net/10016/23407
ISSN: 0377-0427
DOI: 10.1016/j.cam.2014.09.015
UXXI: AR/0000016707
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sobolev_marcellan_JCAM_2015_ps.pdf (684.93 KB)
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2015-08-15
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Elsevier
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Abstract
Orthogonal polynomials on the product domain [a(1), b(1)] x [a(2), b(2)] with respect to the inner product < f, g >(s) = integral(b1)(a1) integral(b2)(a2) del f(x, y) center dot del g(x, y) w(1)(x)w(2)(y) dx dy +lambda f(c(1), c(2))g(c(1), c(2)) are constructed, where w(i) is a weight function on [a(i), b(i)] for i = 1, 2, lambda > 0, and (c(1), c(2)) is a fixed point. The main result shows how an orthogonal basis for such an inner product can be constructed for certain weight functions, in particular, for product Laguerre and product Gegenbauer weight functions, which serve as primary examples.
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Classical orthogonal polynomials, Orthogonal polynomials in two variables, Sobolev inner products, Product domain
Bibliographic citation
Journal of Computational and Applied Mathematics, 2015, v. 284, August, pp. 202-215
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