414 thus there are four unknowns d2 d2 d2 and d2 per

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Unformatted text preview: stimation space. The performance of an error estimate is typically appraised in a given norm by computing an e ectivity index as = kE (x y)k : (7.4.15) ke(x y )k Ideally, the e ectivity index should not di er greatly from unity for a wide range of mesh spacings and polynomial degrees. Bank and Weiser 11] and Oden et al. 17] studied the error estimation procedure (7.4.8) with the simplifying assumption (7.4.14) and were able to establish upper bounds of the form C in the strain energy norm p kekA = A(e e): They could not, however, show that the estimation procedure was asymptotically correct in the sense that ! 1 under mesh re nement or order enrichment. Example 7.4.1. Strouboulis and Haque 19] study the properties of several di erent error estimation procedures. We report results for the residual error estimation procedure (7.4.8, 7.4.14) on the \Gaussian Hill" problem. This problem involves a Dirichlet problem for Poisson's equation on an equilateral triangle having the exact solution u(x y) = 100e;1:5 (x;4:5)2 +(y;2:6)2 ]: Errors are shown in Figure 7.4....
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