# The exact h 1 errors and e ectivity indices at t 05

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Unformatted text preview: .129(-1) 0.977 0.858(-2) 0.985 0.643(-2) 0.989 2 0.872(-3) 0.995 0.218(-3) 0.999 0.963(-4) 0.999 0.544(-4) 1.000 3 0.278(-4) 0.920 0.348(-5) 0.966 0.103(-5) 0.979 0.436(-6) 0.979 4 0.848(-6) 0.999 0.530(-7) 1.000 0.105(-7) 1.000 0.331(-8) 1.000 Table 7.4.2: Errors and e ectivity indices in H 1 for Example 7.4.3 on N -element uniform meshes with piecewise bi-p polynomial bases. Numbers in parentheses indicate a power of ten. The error estimation procedures (7.4.8) and (7.4.9) use average ux values on @ e . As noted, data for such (local) Neumann problems cannot be prescribed arbitrarily. Let us examine this further by concentrating on (7.4.9) which we write as Ae(V E ) = (V r)e+ < V R >e (7.4.19a) 28 Analysis of the Finite Element Method where the elemental residual r was de ned by (7.4.9b) and the boundary residual is R = (pUn )+ ; (pUn);]: (7.4.19b) The function on @ e was taken as 1=2 to obtain (7.4.9a) however, this may not have been a good idea for reasons suggested in Example 7.4.1. Recall (cf. Section 3.1) th...
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