Unformatted text preview: 3 for unifom p-re nement on a mesh of uniform triangular elements having an edge length of 0.25 and for uniform h-re nement with p = 2.
\Extrapolation" refers to the p-re nement procedure described earlier in this section.
This order embedding technique appears to produce accurate error estimates for all polynomial degrees and mesh spacings. The \residual" error estimation procedure is (7.4.8)
with errors at vertices neglected and the hierarchical corrections of order p + 1 forming
S N (7.4.14). The procedure does well for even-degree approximations, but less well for
From (7.4.8), we see that the error estimate E is obtained by solving a Neumann
problem. Such problems are only solvable when the edge loading (the ux average across 24 Analysis of the Finite Element Method Figure 7.4.3: E ectivity indices for several error estimation procedures using uniform hre nement (left) and p-re nement (right) for the Gaussian Hill Problem 19] of Example
element edges) is equilibrated. The ux averaging used in (7.4.8) is, apparently, not
su cient to ensure this when p is odd...
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