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Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems. (English) Zbl 0941.65115
Authors’ abstract: Low-order nonconforming Galerkin methods are analyzed for second-order elliptic equations subjected to Robin, Dirichlet, or Neumann boundary conditions. Both simplicial and rectangular elements are considered in two and three dimensions. The simplicial elements are based on $$P_1$$, as for conforming elements, however, it is necessary to introduce new elements in the rectangular case. Optimal order error estimates are demonstrated in all cases with respect to a broken norm in $$H^1(\Omega)$$ and in the Neumann and Robin cases in $$L_2(\Omega)$$.
Reviewer: P.Burda (Praha)

##### MSC:
 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs 35J25 Boundary value problems for second-order elliptic equations 65F10 Iterative numerical methods for linear systems
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