A discontinuous finite volume method for a coupled fracture model

Abstract

In this paper, we present a discontinuous finite volume method for a hybrid-dimensional coupled fracture model on triangular meshes. In matrix and fracture, the pressure is approximated by the discontinuous and continuous piecewise linear elements, and in order to retain local conservation property, the velocity is sought in the discontinuous lowest-order Raviart–Thomas element space and piecewise linear element space. The proposed numerical scheme is only associated with the pressure, so we avoid solving an indefinite saddle-point problem. In addition, the discontinuous method eliminates the continuity of approximate functions across the interelement boundary, so it has the advantage of high localizability and easy handling of complicated geometries. Optimal order error estimates for the pressure and velocity are proved, and numerical experiments are carried out to confirm our theoretical analysis.