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Domain Decomposition with Nonmatching Grids and Mixed Formulation in the Spaces W 0 1 , p (Ω), W 0 1 (Ω)
Author(s) -
Pousin J.,
Sassi T.
Publication year - 1997
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19970770903
Subject(s) - sobolev space , mathematics , finite element method , domain decomposition methods , a priori and a posteriori , nonlinear system , mathematical analysis , laplace operator , elasticity (physics) , linear elasticity , physics , philosophy , epistemology , quantum mechanics , thermodynamics
In this note, we deal with the domain decomposition method with nonmatching grids for the Laplace operator in the Sobolev space W 0 1,p (Ω) for 2 < p < ∞. Expressing the problem by a mixed formulation, the Brezzi‐Babuška theorem applies (see for example [18]), and we prove that the problem is well posed. A priori error estimates for Lagrangean finite elements of first order are given. Note that the approximate problem can be solved by elimination. This result is straightforwardly extended to the plane linearized elasticity model (see remark 4). This is important when one intents to solve plane nonlinear elasticity problems by using the domain decomposition method with nonmatching grids combined with an adaptive finite element technique based on a posteriori error estimates (see [15]). Please note that the right functional setting for stating nonlinear elasticity problems in the Sobolev space W 1,p with 2 < p.