A note onC
o Galerkin methods for two-point boundary problems |
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Authors: | Miente Bakker |
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Institution: | (1) Mathematisch Centrum, Kruislaan 413, 1098 SJ Amsterdam |
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Abstract: | Summary As is known 4]. theC
o Galerkin solution of a two-point boundary problem using piecewise polynomial functions, hasO(h
2k
) convergence at the knots, wherek is the degree of the finite element space. Also, it can be proved 5] that at specific interior points, the Gauss-Legendre points the gradient hasO(h
k+1) convergence, instead ofO(h
k
). In this note, it is proved that on any segment there arek–1 interior points where the Galerkin solution is ofO(h
k+2), one order better than the global order of convergence. These points are the Lobatto points. |
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Keywords: | AMS(MOS) 65N30 CR: 5 17 |
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