A computational method is presented for the simulation of fluid-driven fracture propagation in a planar crack using unstructured triangular mesh elements. The crack opening elastic interactions between each element are determined using the displacement discontinuity boundary element method. A moving mesh, incorporating appropriate fracture tip asymptotic representations that depend on the fluid viscosity and the fracture toughness, is advanced and periodically regenerated at the crack front. The method includes special logic to represent intermediate viscosity-toughness crack tip asymptotic behaviour. The approach is validated using the simple geometry of a penny-shaped hydraulic fracture and is applied as well to the case of fracture propagation in a discontinuous stress field.