Weighted error estimates of the continuous interior penalty method for singularly perturbed problems

E. Burman, J. Guzman, D. Leykekhman
2008 IMA Journal of Numerical Analysis  
In this paper we analyze local properties of the Continuous Interior Penalty (CIP) Method for a model convection-dominated singularly perturbed convection-diffusion problem. We show weighted a priori error estimates, where the weight function exponentially decays outside the subdomain of interest. This result shows that locally, the CIP method is comparable to the Streamline Diffusion (SD) or the Discontinuous Galerkin (DG) methods.
doi:10.1093/imanum/drn001 fatcat:abvpqtebwzb6lehwm6hddepgsu