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Using splines on triangular mesh to solve PDE with nonhomogeneous boundary

  • 1.

    School of Mathematical Sciences,University of Science and Technology of China,Hefei 230026,China

  • 2.

    Department of Public Foundation, Shanghai University of Finance and Economics Zhejiang College, Jinhua 321013, China

Cite this: JUSTC, 2020, 50(7): 901-905
https://doi.org/10.3969/j.issn.0253-2778.2020.07.005
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  • Received Date: April 19, 2020
  • Revised Date: June 07, 2020
  • Accepted Date: June 07, 2020
  • Published Date: July 30, 2020
    Abstract
  • The spline spaces S,02(Δ(2)mn) defined on type Ⅱ regular triangulation are directly used to solve the PDE problems with homogeneous boundary.For the PDE problems with nonhomogeneous boundary, the solutions obtained usually do not satisfy the convergence properties if they are still solved in the spline spaces S,02(Δ(2)mn),because the basis functions of S,02(Δ(2)mn) vanish on the boundary of the parameter domain. Here, based on the spline spaces S,02(Δ(2)mn) and S2(Δ(2)mn) defined on type Ⅱ regular triangulation,a set of blended spline basis functions were formed by combining the basis functions of S,02(Δ(2)mn) with the basis functions of S2(Δ(2)mn) whose support centers are all outside the boundary of the parameter domain.The blended spline functions were used to solve the PDE problem with nonhomogeneous boundary.Experiment results show that the solutions obtained by this method are convergent.
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