A concurrent global-local numerical method for multiscale parabolic equations

Abstract: This paper presents a concurrent global-local numerical method for solving multiscale parabolic equations in divergence form. The proposed method employs hybrid coefficient to provide accurate macroscopic information while preserving essential microscopic details within specified local defects. Both the macroscopic and microscopic errors have been improved compared to existing results, eliminating the factor of $\Delta t^{-1/2}$ when the diffusion coefficient is time-independent. Numerical experiments demonstrate that the proposed method effectively captures both global and local solution behaviors.