A two-grid decoupled algorithm for fracture models

In this paper, we consider a two-grid decoupled algorithm for two categories of fracture models. In the mixed Darcy/Darcy fracture model, fluid flow in fractures as well as in the surrounding medium is governed by Darcy's law. And in the mixed Darcy-Forchheimer/Darcy fracture model, flow in fractures is governed by Darcy-Forchheimer's law while that in surrounding matrix is governed by Darcy's law. In the proposed two-grid method, we use a coarse grid approximation to the interface coupling conditions for decoupling mixed problems in fractures and surrounding matrix. Error estimates show that the two-grid decoupled algorithm retains the same order of approximation accuracy as the coupled algorithm for the pressure p on H1 semi-norm and the velocity u on (L2)2 norm. Numerical experiments are carried out to verify the accuracy and efficiency of the decoupled algorithm, in which the computation times are reduced greatly compared to the coupled method.