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Unformatted text preview: 1 2) = i N3 ( 1) N3 ( 2)
i = 1 2: Using (7.4.18f) with m = 3 or (2.5.8),
Thus, 1 2 5
N33 ( ) = p ( 2 ; 1):
2 10 2
2
Vi( 1 2) = 58 i ( 1 ; 1)( 2 ; 1)
i = 1 2:
Remark 2. Theorem 7.4.1 applies to tensorproduct bipolynomial bases. Adjerid et
al. 1] show how this theorem can be modi ed for use with hierarchical bases.
Example 7.4.3. Adjerid et al. 2] solve the nonlinear parabolic problem of Example
7.4.2 with q = 20 on uniform square meshes with p ranging from 1 to 4 using the error
estimates (7.4.18a,b) and (7.4.18a,cf). Temporal errors were controlled to be negligible
relative to spatial errors thus, we need not be concerned that this is a parabolic and not
an elliptic problem. The exact H 1 errors and e ectivity indices at t = 0:5 are presented
in Table 7.4.2. Approximate errors are within ten percent of actual for all but one mesh
and appear to be converging at the same rate as the actual errors under mesh re nement. p N = 100
400
900
1600
kek1 =kuk1
kek1 =kuk1
kek1 =kuk1
kek1 =kuk1
1 0.262(1) 0.949 0...
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This document was uploaded on 03/16/2014 for the course CSCI 6860 at Rensselaer Polytechnic Institute.
 Spring '14
 JosephE.Flaherty

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