In this talk, we will present some improvements of continuous interior penalty (CIP) methods on Shishkin rectangular meshes. First of all, we improve the supercloseness result of CIP methods, as depends on a relation between the CIP norm and the streamline diffusion norm in1d. Secondly, we prove the sharpness of this relation. Finally, numerical experiments support our theoretical results.

Dr. Jin Zhang obtained his PhD at Xi’an Jiaotong University in 2013. Currently he is working at Shandong Normal University. His research interests are stabilized finite element methods for convection-dominated problems. More precisely, he is currently working on supercloseness of stabilized finite element methods.