# The functions vix1 x2 vanish on e each function is the

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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 tensor-product bi-polynomial 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,c-f). 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.

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