New homogenization method for diffusion equations

摘要

In this paper, we propose and investigate a new homogenization method for diffusion problems in domains with multiple inclusions with large values of diffusion coefficients. The diffusion problem is approximated by the P1-finite element method on a triangular mesh. The underlying algebraic problem is replaced by a special system with a saddle point matrix. For the solution of the saddle point system we use the typical asymptotic expansion. We prove the error estimates and convergence of the expanded solutions. Numerical results confirm the theoretical conclusions.