Connection between the existence of a priori estimate for a flux and the convergence of iterative methods for diffusion equation with highly varying coefficients
-
George M. Kobelkov
and
Eckart Schnack
Abstract
An iterative method with the number of iterations independent of the coefficient jumps is proposed for the boundary value problem for a diffusion equation with highly varying coefficient. The method applies one solution of the Poisson equation at each step of iteration. In the present paper we extend the class of domains the iterative method is justified for.
Funding statement: The work was supported by INM RAS Division of the Moscow Center for Fundamental and Applied Mathematics (agreement with the Ministry of Science and Higher Education of the Russian Federation No. 075–15–2019–1624/3).
References
[1] G. M. Kobelkov, Iterative solution methods for elliptic boundary value problems. Russ. J. Numer. Anal. Math. Modelling 35 (2020), No. 4, 1–8.10.1515/rnam-2020-0018Search in Google Scholar
[2] G. M. Kobelkov, Solution of equations with highly varying coefficients. Preprint No. 145. Comput. Math. Dept. of Acad. Sci. USSR, Moscow, 1987 (in Russian).Search in Google Scholar
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- Frontmatter
- Variational data assimilation for a sea dynamics model
- Connection between the existence of a priori estimate for a flux and the convergence of iterative methods for diffusion equation with highly varying coefficients
- Mesh scheme for a phase transition problem with time-fractional derivative
- A finite element scheme for the numerical solution of the Navier–Stokes/Biot coupled problem
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Articles in the same Issue
- Frontmatter
- Variational data assimilation for a sea dynamics model
- Connection between the existence of a priori estimate for a flux and the convergence of iterative methods for diffusion equation with highly varying coefficients
- Mesh scheme for a phase transition problem with time-fractional derivative
- A finite element scheme for the numerical solution of the Navier–Stokes/Biot coupled problem
- Difference schemes for second-order ordinary differential equations with corrector and predictor properties
