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Abstract: This paper is organized as follows. In the next section, we introduce the elliptic and finite element problems. Section 3 contains a discussion of a vertex-based method that works well in two dimensions. Our new algorithm is introduced in Section 4 and is briefly contrasted with those of Bramble, Pasciak, and Schatz [3] and Mandel [7], [8]. Finally, in Section 5, we state and prove our theoretical results. (Update)
Context of citations to this paper: More
.... replaced by an approximation that is cheaper to invert and with various selections of the spaces V i , see the discussion and references in [9, 15, 23]. 3. PRINCIPLES OF STRATEGY SELECTION The key observation here is the P.L. Lions Lemma [3, 8] which states that if there is...
...that these constants may depend on the constant in (22) or on the regularity of the triangulation, but they are independent of h and H. Following [4] 12] or [22], define the scaled Sobolev norms i ; kuk jru(x)j dx; j u j j u(t) Gamma u(s) j j t Gamma s j dtds: The advantage...
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BibTeX entry: (Update)
Smith B. F. (1991) A domain decomposition algorithm for elliptic problems in three dimensions. Numer. Math. 60(2): 210234. http://citeseer.ist.psu.edu/article/smith90domain.html More
@article{ smith91domain,
author = "Barry F. Smith",
title = "A Domain Decomposition Algorithm for Elliptic Problems in Three Dimensions",
journal = "Numerische Mathematik",
volume = "60",
number = "2",
pages = "219--234",
year = "1991",
url = "citeseer.ist.psu.edu/article/smith90domain.html" }
Citations (may not include all citations):689 The Finite Element Method for Elliptic Problems (context) - Ciarlet - 1978
233 The construction of preconditioners for elliptic problems by.. (context) - Bramble, Pasciak et al. - 1986
42 Some domain decomposition algorithms for elliptic problems (context) - Dryja, Widlund - 1989
30 A method of domain decomposition for 3-D finite element prob.. (context) - Dryja - 1988
23 An optimal domain decomposition preconditioner for the finit.. (context) - Smith - 1989
18 Iterative solvers by substructuring for the p-version finite.. (context) - Mandel - 1990
7 A second order finite difference analogue of the first bihar.. (context) - Bramble - 1966
5 Methods Engrg (context) - decomposition, the et al. - 1990
1 Courant Institute (context) - Algorithms, Partial et al. - 1990
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