Piecewise Polynomial Collocation for Boundary Integral Equations

@article{Atkinson1995PiecewisePC,
  title={Piecewise Polynomial Collocation for Boundary Integral Equations},
  author={Kendall E. Atkinson and David Da-Kwun Chien},
  journal={SIAM J. Scientific Computing},
  year={1995},
  volume={16},
  pages={651-681}
}
This paper considers the numerical solution of boundary integral equations of the second kind, for Laplace's equation u = 0 on connected regions D in R 3 with boundary S. T h e boundary S is allowed to be smooth or piecewise smoothh and we l e t f K j 1 K N g be a triangulation o f S. T h e n umerical method is collocation with approximations w h i c h are piecewise quadratic in the parametrization variables, leading to a numerical solution u N : Superconvergence results for u N are given for S… CONTINUE READING

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