A Posteriori Error Control for DPG Methods

@article{Carstensen2014APE,
  title={A Posteriori Error Control for DPG Methods},
  author={Carsten Carstensen and Leszek F. Demkowicz and Jayadeep Gopalakrishnan},
  journal={SIAM J. Numerical Analysis},
  year={2014},
  volume={52},
  pages={1335-1353}
}
A combination of ideas in least-squares finite element methods with those of hybridized methods recently led to discontinuous Petrov–Galerkin (DPG) finite element methods. They minimize a residual inherited from a piecewise ultraweak formulation in a nonstandard, locally computable, dual norm. This paper establishes a general a posteriori error analysis for the natural norms of the DPG schemes under conditions equivalent to a priori stability estimates. It is proven that the locally computable… CONTINUE READING