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DG Treatment of Non-Conforming Interfaces in 3D Curl-Curl Problems

by R. Casagrande and C. Winkelmann and R. Hiptmair and J. Ostrowski

(Report number 2014-32)

Abstract
We consider 3D Curl-Curl type of problems in the presence of arbitrary,non-conforming mesh-interfaces. The Interior Penalty/Nitsche’s Method is ex-tended to these problems for edge functions of the first kind. We present an a priori error estimate which indicates that one order of convergence is lost in comparison to conforming meshes due to insufficient approximation properties of edge functions. This estimate is sharp for first order edge functions: In a numerical experiment the method does not converge as the mesh is refined.

Keywords: Discontinuous Galerkin, Sliding Interface, Non-Conforming Mesh, FEM, Magnetostatics, Curl-Curl Operator, Interior Penalty

@Techreport{CWHO14_582,
  author = {R. Casagrande and C. Winkelmann and R. Hiptmair and J. Ostrowski},
  title = {DG Treatment of Non-Conforming Interfaces in 3D Curl-Curl Problems},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2014-32},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2014/2014-32.pdf },
  year = {2014}
}

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