A posteriori error estimates for mixed-dimensional Darcy flow using non-matching grids

Source abstract

Abstract In this article, we extend the a posteriori error estimates for hierarchical mixed-dimensional elliptic equations developed in [Varela et al., J. Numer. Math. , 31 (2023), pp. 247–280] to the setting of non-matching mixed-dimensional grids. The extension is achieved by introducing transfer grids between the planar subdomain and interface grids, together with stable discrete projection operators for primal (potential) and dual (flux) variables and grid mismatch operators. The proposed estimators remain guaranteed, reliable and fully computable for locally mass-conservative approximations. Numerical experiments, including three-dimensional problems based on community benchmarks for incompressible Darcy flow in fractured porous media, demonstrate reliable performance of the estimators for the non-matching grids and effectivity that is comparable to the estimators previously obtained for matching grids.