A Posteriori Error Estimates for Hypersingular Integral Equation on Spheres with Spherical Splines

  • Duong Thanh PhamEmail author
  • Tung Le


A posteriori residual and hierarchical upper bounds for the error estimates are proved when solving the hypersingular integral equation on the unit sphere by using the Galerkin method with spherical splines. Based on these a posteriori error estimates, adaptive mesh refining procedures are used to reduce complexity and computational cost of the discrete problems. Numerical experiments illustrate our theoretical results.


Hypersingular integral equation Spherical spline A posteriori error estimate Adaptivity 

Mathematics Subject Classification (2010)

65N30 65N38 65N15 65N50 


Funding Information

This research is funded by the Vietnam National Foundation for Science and Technology Development (NAFOSTED) under grant no. 101.99–2016.13. A part of this research was conducted during the first author’s 2-month visit to the Vietnam Insitute for Advanced Study in Mathematics (VIASM). The authors would like to thank VIASM for the supports.


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Copyright information

© Institute of Mathematics, Vietnam Academy of Science and Technology (VAST) and Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  1. 1.Vietnamese German UniversityBinh Duong New CityVietnam

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