Enhancement of the accuracy of the Green element method: Application to potential problems

► The accuracy of the Green element method (GEM) is improved with a new formulation. ► The formulation uses a second order difference approximation of internal fluxes. ► This new formulation is implemented on rectangular and triangular elements. ► The formulation is applied to six examples of linear and nonlinear potential flows. ► The accuracy of the formulation is comparable to flux-based formulations.