A Posteriori Error Estimates for Discontinuous Galerkin Methods Using Non-polynomial Basis Functions Part I : Second Order Linear Pde

@inproceedings{Lin2016APE,
  title={A Posteriori Error Estimates for Discontinuous Galerkin Methods Using Non-polynomial Basis Functions Part I : Second Order Linear Pde},
  author={Lin Lin and Benjamin Stamm},
  year={2016}
}
Abstract. We present the first systematic work for deriving a posteriori error estimates for general non-polynomial basis functions in an interior penalty discontinuous Galerkin (DG) formulation for solving second order linear PDEs. Our residual type upper and lower bound error estimates measure the error in the energy norm. The main merit of our method is that the method is parameter-free, in the sense that all but one solution-dependent constants appearing in the upper and lower bound… CONTINUE READING