Discontinuous Galerkin method for an elliptic problem with nonlinear Newton boundary conditions in a polygon

@article{Feistauer2019DiscontinuousGM,
  title={Discontinuous Galerkin method for an elliptic problem with nonlinear Newton boundary conditions in a polygon},
  author={Miloslav Feistauer and Filip Roskovec and Anna‐Margarete S{\"a}ndig},
  journal={Ima Journal of Numerical Analysis},
  year={2019},
  volume={39},
  pages={423-453}
}
The paper is concerned with the analysis of the discontinuous Galerkin method (DGM) for the numerical solution of an elliptic boundary value problem with a nonlinear Newton boundary condition in a two-dimensional polygonal domain. Using the monotone operator theory it is possible to prove the existence and uniqueness of the exact weak solution and the approximate DG solution. The main attention is paid to the study of error estimates. To this end, the regularity of the weak solution is… 

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