Adaptive Numerical Treatment of Elliptic Systems on Manifolds

@article{Holst2001AdaptiveNT,
  title={Adaptive Numerical Treatment of Elliptic Systems on Manifolds},
  author={Michael J. Holst},
  journal={Adv. Comput. Math.},
  year={2001},
  volume={15},
  pages={139-191}
}
Adaptive multilevel finite element methods are developed and analyzed for certain elliptic systems arising in geometric analysis and general relativity. This class of nonlinear elliptic systems of tensor equations on manifolds is first reviewed, and then adaptive multilevel finite element methods for approximating solutions to this class of problems are considered in some detail. Two a posteriori error indicators are derived, based on local residuals and on global linearized adjoint or dual… CONTINUE READING

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