By Anatoliĭ Antonevich, Yakov Radyno (auth.), Prof. Dr. Lothar Jentsch, Prof. Dr. Fredi Tröltzsch (eds.)
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35-40 (1986). : On the multistep time discretization of linear initial-boundary value problems and their boundary integral equations. Numer. Math. 67, 365-390 (1994). : Time discretization of parabolic boundary integral equations. Numer. Math. 63, 455-481 (1992). : Une methode variationnelle d'elements finis pour la resolution numerique d'un probleme exterieur dans R,3. RAIRO 7, 105-129 (1973). [22] Noon, P. : The single layer heat potential and Galerkin boundary element methods for the heat equation.
Q(S). Let us consider, e. , a > 1/2 and q = 2. flh' Vh E X h, the inverse inequality and the uniform boundedness of Uh in W 1,2(nh), we find that the error of numerical integration is of order 0(1). Hence, the convergence is not guaranteed. Therefore, we try to "overintegrate", i. , we use a quadrature formula with k = 2. Then we can find that the numerical integration error is of order O(hl-a/r) with r ? 1, which yields the convergence for any r E (a, 00). We see that we "lose more than one order" because of the nonlinearity on the boundary.
Let an elastic medium with crack and prescribed loads be given. 4). We arrived at the variational principle that coincides with the one established in [3] considered for the same set. The proof of Statement 5 demonstrates the equivalence of two approaches to construct the solution for the problem of a cavity (a crack-cut) with contact regions: The one proposed in the present work (section 3) and the one based on the extremality property of elastic energy U are equivalent. We now show that both approaches lead to the construction of a solution, which is nonsingular near the boundary of the contact region.