A concurrent global-local numerical method for multiscale parabolic equations
For researchers solving multiscale parabolic equations, this method offers improved error bounds, but the improvement is incremental over existing approaches.
This paper introduces a concurrent global-local numerical method for multiscale parabolic equations that improves both macroscopic and microscopic errors by eliminating the Δt^{-1/2} factor for time-independent diffusion coefficients. Numerical experiments show effective capture of global and local solution behaviors.
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 $Δt^{-1/2}$ when the diffusion coefficient is time-independent. Numerical experiments demonstrate that the proposed method effectively captures both global and local solution behaviors.