A node-centered finite volume method for a fracture model on triangulations

In this paper, a node-centered finite volume method based on triangulations for a fracture model is presented, in which we restrict the pressure to the linear finite element space while the velocity can be approximated by constant vectors element by element. The numerical scheme is established just associated with the pressure to avoid the saddle-point problem. Error estimates of O(h) accuracy for the discrete H1 semi-norm and the discrete L2 norm of pressure p and the (L2)2 norm of velocity u are developed on general triangulations. Under an additional assumption about essentially symmetric control volumes, the error estimates for the pressure p can be improved to O(h3/2). Finally, numerical experiments are carried out to verify the accuracy and convergence rates for the proposed finite volume scheme.