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By F Paul Esposito; Louis Witten

ISBN-10: 0306310228

ISBN-13: 9780306310225

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Meths . Engrg . 43, 997-1016 10. , Tezaur R (2000) Finite element solution of two-dimensional acoustic scattering problems using arbitrarily shaped convex artificial boundaries. J. of Comput. Acou. 8, 81-100 11. , Djellouli R. (submitted) Three-dimensional finite element calculations in acoustic scattering using arbitrarily shaped convex artificial boundaries. Internat. J. Numer. Meths . Engrg . 12. , Sauter S. (1997) Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers?

In this special case we establish a constant lower bound. We then discuss the case without a N - D ordering and show a weaker bound containing two logarithmic factors . 1 The Neumann-Dirichlet Case We note that for the N - D ordering the matrix B in (8), cf. (9), can be rewritten in the form (32) where I is an identity matrix of order equal to the dimension of V = Im(B)j it corresponds to the Dirichlet substructures {}i . The block diagonal matrix BN corresponds to the Neumann substructures and the only nonzero blocks equal Bi~(i) B'Y",w which correspond to the edges 8m (i) = 'Ym(j) j see (9).

Comparing the theoretical estimates obtained for the dualprimal FETI algorithm with just face constraints with the algorithms based on edge constraints which are proposed and analyzed in [11], reveals subtle differences which seem to indicate that the edge based algorithms are more powerful in the case of general distributions of the jumps in the coefficients . , Lagrange multipliers, as in a dual method. Recently, there have been also extensions of the dual-primal FETI method to mortar finite element methods, cf.

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Asymptotic structure of space-time : [proceedings of a Symposium on Asymptotic Structure of Space-Time (SOASST), held at the University of Cincinnati, Ohio, June 14-18, 1976] by F Paul Esposito; Louis Witten


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