Published

Convergence and optimality of adaptive mixed finite element methods

Long Chen, Michael Holst, and Jinchao Xu

Mathematics of Computation. (78) 35-53, 2009.

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ABSTRACT:

  The convergence and optimality of adaptive mixed finite element
  methods for the Poisson equation are established in this paper. The
  main difficulty for the mixed finite element method is the lack of
  minimization principle and thus the failure of orthogonality. A
  quasi-orthogonality property is proved using the fact that the error
  is orthogonal to the divergence free subspace, while the part of the
  error containing divergence can be bounded by the data oscillation
  using a discrete stability result. This discrete stability sresult
  is also used to get a localized discrete upper bound which is
  crucial for the proof of the optimality of the adaptive
  approximation.