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Iterative solution methods for elliptic boundary value problems

  • Georgy M. Kobelkov EMAIL logo
Published/Copyright: August 13, 2020

Abstract

For elliptic boundary value problems (the diffusion equation and elasticity theory ones) with highly varying coefficients, there are proposed iterative methods with the number of iterations independent of the coefficient jumps. In the differential case these methods take solving the boundary value problem for the Poisson equation at each step of iterations while in the finite difference (finite element) approximation it is possible to use another operator as a preconditioner.

MSC 2010: 35J25; 35J47; 65N12
  1. Funding: The work was supported by the Moscow Center of Fundamental and Applied Mathematics (Agreement with the Russian Ministry of Education and Science No. 075–15–2019–1624).

References

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Received: 2020-04-30
Accepted: 2020-05-22
Published Online: 2020-08-13
Published in Print: 2020-08-26

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