New asymptotic expansion for the diffusion problem with high-contrast inclusions: Numerical results

作者：Kramarenko, V K^*; Kuznetsov, Yu A

来源：Journal of Computational and Applied Mathematics, 2020, 365: UNSP 112363.

DOI：10.1016/j.cam.2019.112363

• Diffusion equation
• High-contrast inclusions
• Finite elements
• Asymptotic expansions
• Saddle-point matrix

This paper is concerned with the new approach to the numerical solution of diffusion equations with high contrast coefficients. The classical P1 finite element system of equations is replaced by the equivalent system of the saddle point type. For the saddle point problem a new recently invented asymptotic expansion with respect to a small parameter is discussed and the estimates for the convergence factor are given. Numerical results completely confirm the theoretical accuracy and convergence results for the considered method.