Abstract
This study concerns the Darcy flow problem in a two-dimensional fractured porous domain, in which the fracture is regarded as a one-dimensional interface, interacting with the surrounding media. In this paper, a finite volume element method (FVEM) is first proposed for the multi-dimensional fracture model, and error estimates for the pressure with optimal convergence are discussed. On this basis, a two-grid FVEM is developed for decoupling the multi-domain fracture model by a coarse grid approximation to the interface coupling conditions, and theoretical analysis demonstrates that approximation accuracy does not deteriorate under the two-grid decoupling technique. Finally, numerical experiments for FVEM and two-grid FVEM are presented to confirm the accuracy of theoretical analysis.
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