Journal of Scientific Computing

, Volume 66, Issue 1, pp 1–18 | Cite as

The Highest Superconvergence of the Tri-linear Element for Schr\(\ddot{\text {o}}\)dinger Operator with Singularity

  • Wenming He
  • Zhimin Zhang
  • Ren Zhao


In this paper, the eigenvalues for Schr\(\ddot{\text {o}}\)dinger operator with singularity are analyzed. A special piecewise uniform rectangular partition is constructed and it has been proven that, under this partition, the tri-linear rectangular finite element method has the highest possible superconvergence rate for eigenvalue.


Schr\(\ddot{\text {o}}\)dinger operator Richardson extrapolation The highest superconvergence 

Mathematics Subject Classification

65N25 65N30 65N15 


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Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  1. 1.Department of MathematicsWenzhou UniversityWenzhouPeople‘s Republic of China
  2. 2.Department of MathematicsWayne State UniversityDetroitUSA

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