Although this is a time dependent problem which we

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Unformatted text preview: es of N triangles with polynomial degrees p ranging from 1 to 4. ~ The results with S N consisting only of hierarchical corrections of degree p + 1 are reasonable. E ectivity indices are in excess of 0.9 for the lower-degree polynomials p = 7.4. A Posteriori Error Estimation ~ p SN 1 2 3 4 8 2 1.228 3 0.948 4 0.951 4, 2 3.766 5 0.650 5, 3 0.812 25 N 32 1.066 0.993 0.938 1.734 0.785 0.911 128 1.019 0.998 0.938 1.221 0.802 0.920 512 1.005 0.999 0.938 1.039 0.803 0.925 Table 7.4.1: E ectivity indices in H 1 at t = 0:06 for Example 7.4.2. The degrees of the ~ hierarchical modes used for S N are indicated in that column 4]. 1 2, but degrade with increasing polynomial degree. The addition of a lower (third) degree polynomial correction has improved the error estimates with p = 4 however, a similar tactic provided little improvement with p = 3. These results and those of Strouboulis and Haque 19] show that the performance of a posteriori error estimates is still dependent on the problem being solved and on the mesh used to solve it. Another way of simplifying the error estimation procedure (7.4.8) and of understanding the di erences betw...
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