A Class of Discontinuous Petrov-Galerkin Methods . Part III : Adaptivity

  title={A Class of Discontinuous Petrov-Galerkin Methods . Part III : Adaptivity},
  author={Leszek F. Demkowicz and Jay Gopalakrishnan and Antti H. Niemi},
We continue our theoretical and numerical study on the Discontinuous Petrov-Galerkin method with optimal test functions in context of 1D and 2D convection-dominated diffusion problems and hp-adaptivity. With a proper choice of the norm for the test space, we prove robustness (uniform stability with respect to the diffusion parameter) and mesh-independence of the energy norm of the FE error for the 1D problem. With hp-adaptivity and a proper scaling of the norms for the test functions, we… CONTINUE READING
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