Error Control and Adaptivity for Heterogeneous Multiscale Approximations of Nonlinear Monotone Problems

@inproceedings{Henning2014ErrorCA,
  title={Error Control and Adaptivity for Heterogeneous Multiscale Approximations of Nonlinear Monotone Problems},
  author={Patrick Henning and Mario Ohlberger},
  year={2014}
}
In this work we introduce and analyse a new adaptive PetrovGalerkin heterogeneous multiscale finite element method (HMM) for monotone elliptic operators with rapid oscillations. In a general heterogeneous setting we prove convergence of the HMM approximations to the solution of a macroscopic limit equation. The major new contribution of this work is an a-posteriori error estimate for the L2-error between the HMM approximation and the solution of the macroscopic limit equation. The a posteriori… CONTINUE READING
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