Improved linear trial function finite element model of soil moisture transport

Two methods of modeling a higher‐order approximation function of soil moisture transport by an improved linear trial function approximation are presented. The first approach considered is based upon use of the alternation theorem and a finite element capacitance matrix that incorporates the Galerkin finite element, subdomain, finite difference, and proposed nodal domain integration methods. The second approach extends the first approach by developing a temporal relationship for element matrices such that a higher‐order approximation function can be modeled by a linear approximation function. Comparison of model results produced from a nodal domain integration model incorporating these improved linear trial function approximations to the finite element, subdomain, and finite difference methods indicates that this approach may lead to a generalized modeling method for soil moisture transport problems.