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The Application of a Special Hermite Finite Element Coupled with Collocation to the Diffusion Equation

  • Lidiya Gileva
  • Evgeniya KarepovaEmail author
  • Vladimir Shaydurov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11386)

Abstract

In the paper, we propose an efficient method based on the use of a bicubic Hermite finite element coupled with collocation for the diffusion equation. This enables one to reduce the dimension of the system of equations in comparison with the standard finite element scheme. Numerical experiments confirm a theoretical convergence estimate and demonstrate the advantage of the proposed method.

Keywords

Diffusion equation Finite element method Hermite finite element Collocation method 

Notes

Acknowledgements

Supported by Project 17-01-00270 of Russian Foundation for Basic Research.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Institute of Computational Modelling of SB RASAkademgorodok, KrasnoyarskRussia
  2. 2.Siberian Federal UniversityKrasnoyarskRussia

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