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**Sample text**

Again, the truncated basis performs best for either method. Finally, for this example in the right of ﬁgure the error reduction for the exact active set strategy can be seen. We note, that at least 100 instead of 18 multigrid cycles are necessary when compared to the monotone multigrid method. We now investigate the mesh-dependence of our solution strategies. 973 elements and set N = 5 in (12). In Table 1, the number of iteration steps for the case of equal normals (left number in each column) and outer normals (right number) are shown for Algorithm 1 with Splittings 1-4.

The temperature part of the algebraic saddle point system has the form .. .. . 0 . . (5) . . AˆSS D θˆS = rS , θθ 0 0 Id −Dλm λθ 46 S. I. Wohlmuth where the nonlinearity in the heat law enters in terms of Dλm . Static condensation of the heat ﬂux in (5) yields for the second line of (5) −1 ˆ . . + AˆSS θθ + DDλm θS = rS . To handle the nonlinearity in Dλm we use an inexact ﬁxed point iteration. Mortar methods for contact problems 47 We consider the problem depicted in the left picture of Figure 6.

For details of the algorithm we refer to [8]. To show the performance of the algorithm, we consider a frictionless contact problem for a linearized St. Venant–Kirchhoﬀ material in the 3D case. In the left picture of Figure 1, a cross section of the problem deﬁnition is shown. The lower domain Ωm models a half-bowl which is ﬁxed at the outer boundary as shown in the left picture of Figure 1. Against this bowl, we press Mortar methods for contact problems 41 d h Ωs r ri ra Ωm Fig. 1. Left: problem deﬁnition; middle: cut through the distorted domains with the eﬀective von Mises stress on level 3; right: contact stress λh · n on level 3.

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