A coupled finite element method for the numerical simulation of hydraulic fracturing with a condensation technique

Computation cost is a key issue for finite element methods to simulate hydraulic fracturing. In this paper a coupled finite element method combined with a condensation technique is proposed to address this issue. Removing the node displacements that have no contribution to fracture widths from the coupled equations, the condensation technique reduces the size of the coupled equations in the proposed method. The numerical method with the condensation technique is verified. Simulations show that the condensation technique can reduce the computation cost effectively, in particular when the fracture propagation regime is viscosity-dominated or the simulation is on the early stage. The effects of the condensation technique on the simulation accuracy, stability, and convergence of the numerical method are discussed. The condensation technique is applicable to other finite element methods that are based on linear elastic fracture mechanics.