Nonconforming Galerkin methods based on quadrilateral elements for second order elliptic problems
TLDR
In this paper, low-order nonconforming Galerkin methods are analyzed for second-order elliptic equations subjected to Robin, Dirichlet, or Neumann boundary conditions in two and three dimensions.Abstract:
Low-order nonconforming Galerkin methods will be analyzed for second-order elliptic equations subjected to Robin, Dirichlet, or Neumann boundary conditions. Both simplicial and rectangular elements will be considered in two and three dimensions. The simplicial elements will be 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 (Ω) and in the Neumann and Robin cases in L 2 (Ω).read more
Citations
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References
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The Mathematical Theory of Finite Element Methods
TL;DR: In this article, the construction of a finite element of space in Sobolev spaces has been studied in the context of operator-interpolation theory in n-dimensional variational problems.
Journal ArticleDOI
Conforming and nonconforming finite element methods for solving the stationary Stokes equations I
M. Crouzeix,P.-A. Raviart +1 more
TL;DR: Both conforming and nonconforming finite element methods are studied and various examples of simplicial éléments well suited for the numerical treatment of the incompressibility condition are given.
Journal ArticleDOI
Mixed and nonconforming finite element methods : implementation, postprocessing and error estimates
Douglas N. Arnold,Franco Brezzi +1 more
TL;DR: In this paper, a technique d'implantation de certains elements finis mixtes bases on l'utilisation des multiplicateurs de Lagrange utilises for imposer la continuite a la traversee des elements.
Journal ArticleDOI
Simple nonconforming quadrilateral Stokes element
Rolf Rannacher,Stefan Turek +1 more
TL;DR: In this paper, a simple nonconforming quadrilateral Stokes element based on "rotated" multi-linear shape functions is analyzed, and it is shown that on strongly nonuniform meshes the usual parametric version of this element suffers from a lack of consistency, while its nonparametric counterpart turns out to be convergent with optimal orders.