Rayleigh‐Ritz and Galerkin finite elements for diffusion‐convection problems

Finite element methods are presented for the solution of certain two‐dimensional partial differential equations of interest in water resource problems. Earlier work using Galerkin's method for one‐dimensional problems is shown to be a prototype finite element technique. It is suggested that previous variational (Rayleigh‐Ritz) formulations of finite elements for some problems are misleading and are of limited application when compared with Galerkin's method. The accuracy and stability of the techniques presented are discussed in relation to the well‐known ‘numerical diffusion and dispersion’ phenomena prevalent in popular finite difference methods.