Galerkin finite element method and the groundwater flow equation: 1. Convergence of the method

This paper is concerned with the convergence of the Galerkin finite element method applied to a groundwater flow problem containing a borehole, with special reference to quadrature effects and the accuracy of the solution. It is shown that there exists an optimal quadrature rule for every choice of piecewise polynomial basis functions. Another interesting result proved here is that, in a direct application of the method the accuracy is very nearly independent of the degree of the polynomial basis functions, but strongly dependent on the distance of the borehole from the boundary if this is small.