A quadratic Petrov‐Galerkin Solution for kinematic wave overland flow

Abstract

A Petrov‐Galerkin (PG) finite element method was developed to solve the kinematic wave formulation of the overland flow equations. The resultant model uses quadratic basis functions and test functions that are modified by polynomials of cubic and quartic order, yielding a formulation that includes four PH parameters. The PG model was found to reduce the mean sum of square error of the solution compared to a conventional Bubnov‐Galerkin finite element solution by about a factor of 3 as the Courant number (Cr) approached one. Good results were also achieved with the PG method for problems that resulted in shock formation, which are typical of many applied problems of concern. PG parameters were found to depend strongly upon the Courant number and weakly upon the number of nodes in the system. Polynomial expressions were derived to approximate the PG parameters over the range 0 < Cr < 1. As the number of nodes in the system increased, a single‐parameter version of the model yielded solutions approaching the accuracy of the four‐parameter model.