### Table 2. Relative L2 and energy error norms for the patch test on convex polygonal meshes

in Summary

"... In PAGE 28: ... For the Laplace shape functions, numerical integration is done on the reference element (Figure 18b), whereas for all other interpolation schemes, the physical element (Figure 18a) is used in the numerical integration. The relative L2 and energy error norms for the convex polygonal elements are presented in Table2 . The Laplace interpolant provides the most... ..."

### TABLE VIII. Crambin Fragment Energies and Timings for Different Resolutions and Grid Sizes for FD Calculations.

1996

### Table 1: Comparison of convergence results for the energy and other crucial quantities for

1998

"... In PAGE 3: ... However, for the present problem of a non-convex energy density, the results are rather sobering: In general, it can only be shown that a minimizing deformation u h 2A h satisn0ces En28u h n29 n14 Ch 1=2 ; n2810n29 where C denotes a generic constant that may depend on the topology of the quasiuniform triangulation T h and the domain n0a but not on the mesh-size h, see n5b8, 18, 17n5d, and n5b7n5d for a den0cnition of quasiuniformity.For a complete list of results for important quantities, see Table1 above. Moreover, it turns out that the quality of the approximation depends strongly... In PAGE 4: ... To this end, we present a new algorithm based on discontinuous n0cnite elements. It will be shown that this algorithm allows much improved convergence rate estimates for the energy, namely On28h 2 n29, and other quantities of interest as they are given in Table1 . In particular, the resolution of laminate microstructure on general meshes is much better than by the classical n28non-n29conforming discussed above.... In PAGE 7: ... The earlier case cancels out the contribution from the n28scaled, squaredn29 L 2 -norm of the deformation on the interior n0cnite elements and gives rise to an energy functional that is rotationally invariant, whereas the latter case is not rotationally invariant anymore, but allows for better approximation of the volume fractions. Again, we stress the fact that these convergence results are much better than those derived for the conforming n28using n28bi-, tri-n29linear ansatz functions, see n5b18n5dn29 or classical nonconforming n28using piecewise rotated n28bi-,trin29linear ansatz functions, see n5b18, 16n5dn29 n0cnite element methods, see also Table1 . This ren0dects the increased accuracy of the ansatz for non-aligned meshes: The misaligned triangulation does not lead to a dramatic pollution of the computed solution anymore.... ..."

Cited by 5

### Table 1 Convex

"... In PAGE 4: ... The next step of the analysis, however, provided a more promising result. As shown in Table1 , the number of people visible from each convex space was consistently correlated not only with the visual range of the space but also with its integration into the setting as a whole. That more people are visible from spaces which have a stronger visual range is hardly surprising.... In PAGE 5: ... However, these correlations were neither very strong or consistent. Table1 . Correlation between the Number of People Visible from Each Convex Space with Convex Configuration Variables.... ..."

### Table 3 Convex Axial

"... In PAGE 6: ...486 Note. For explanation of variables see notes to Table 1 Tracking frequencies, by contrast, were most clearly and consistently correlated with connectivity, as indicated by Table3 . These correlations were not only significant statistically but also quite strong.... In PAGE 6: ... Table3 . Correlation between Tracking Frequency and Configuration Variables.... ..."

### Table 1: Properties of Convex-Hull and Convex sets.

1994

"... In PAGE 2: ... 100]), meaning that the conventional Convex-Hull is indeed a particular case of the generalized Convex-Hull. Table1 shows that some of the basic properties of the Convex-Hull and of Convex sets are naturally extended to the B-Convex-Hull operation and to B-Convex sets.... ..."

Cited by 1

### Table 1: Comparison of convergence results for the energy and other crucial quantities for di erent nite element methods. See the text for explanation of the notation.

1998

"... In PAGE 3: ... However, for the present problem of a non-convex energy density, the results are rather sobering: In general, it can only be shown that a minimizing deformation uh 2 Ah satis es E(uh) Ch1=2; (10) where C denotes a generic constant that may depend on the topology of the quasiuniform triangulation Th and the domain but not on the mesh-size h, see [8, 21, 22], and [7] for a de nition of quasiuniformity. For a complete list of results for important quantities, see Table1 . Moreover, it turns out that the quality of the approximation depends strongly on the degree of alignment of the numerical mesh with the physical laminates.... In PAGE 4: ... To this end, we present a new algorithm based on discontinuous nite elements. It will be shown that this algorithm allows much improved convergence rate estimates for the energy, namely O(h2), and other quantities of interest as they are given in Table1 . In particular, the resolution of laminate microstructure on general meshes is much better than by the classical (non-)conforming discussed above.... In PAGE 7: ... In the case (d), it additionally depends on the choice of the value of . Again, we stress the fact that these convergence results are much better than those derived for the conforming (using (bi-, tri-)linear ansatz functions, see [21]) or classical non-conforming (using piecewise rotated (bi-,tri)linear ansatz functions, see [20, 21]) nite element methods, see also Table1 . This re ects the increased accuracy of the ansatz for non-aligned meshes: The misaligned triangulation does not lead to a dramatic pollution of the computed solution anymore.... ..."

Cited by 5

### Table 1: Values of the convex aggregation.

"... In PAGE 7: ... None of the images was misclassified. The values for the aggregation are in Table1 . The corresponding boosting map is shown in Fig 5.... ..."