Convergence and optimality of adaptive mixed finite element methods

@article{Chen2009ConvergenceAO,
  title={Convergence and optimality of adaptive mixed finite element methods},
  author={Long Chen and Michael J. Holst and Jinchao Xu},
  journal={Math. Comput.},
  year={2009},
  volume={78},
  pages={35-53}
}
  • Long Chen, Michael J. Holst, Jinchao Xu
  • Published in Math. Comput. 2009
  • Mathematics, Computer Science
  • The convergence and optimality of adaptive mixed finite element methods for the Poisson equation are established in this paper. The main difficulty for mixed finite element methods 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 that is not divergence free can be bounded by the data oscillation using a discrete stability… CONTINUE READING

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