Least‐squares characteristics and finite elements for advection–dispersion simulation

The method of characteristics is combined with the method of least‐squares to solve the advection equation within the finite element framework. Fourier mode analysis shows that the numerical scheme is stable and accurate even when a linear basis function is used. However, in practical application, the involvement of using numerical quadrature in this method can produce numerical instability, depending on the value of the Courant number used. It is found that using C1 continuous Hermitian cubic basis functions in the scheme reduces the degree of instability significantly and produces high accuracy. When being used in a split‐operator approach, this method combines naturally with the standard finite element method and results in a highly accurate scheme for advection–dispersion simulation.