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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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