Nepomnyashchikh, S. V. Finite-element trace theorems. (English) Zbl 0960.65129 Bull. Novosib. Comput. Cent., Ser. Numer. Anal. 2000, No. 9, 69-75 (2000). The author proves the finite-element trace theorem for the Sobolev spaces \(H^1_{p,q}\) and then studies the properties of Poincaré-Steklov operators for anisotropic elliptic problems.The main aim of the article is to study the space of the traces of the finite-element functions on the boundaries of a bounded polygonal domain \(\Omega\) which is generated by the \(H_{p,q}^1(\Omega)\) norm. The author proves that the corresponding constants in the trace theorems are independent of the parameters. Sobolev spaces with parameter-dependent norms are generated, for instance, by elliptic problems with disproportional anisotropic coefficients. These results are used for obtaining effective domain decomposition methods. Reviewer: V.Grebenev (Novosibirsk) MSC: 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems 65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations Keywords:finite-element; trace theorem; domain decomposition; anisotropic elliptic problem; Sobolev spaces; Poincaré-Steklov operator PDFBibTeX XMLCite \textit{S. V. Nepomnyashchikh}, Bull. Novosib. Comput. Cent., Ser. Numer. Anal. 2000, No. 9, 69--75 (2000; Zbl 0960.65129)