Computational issues and applications of line-elements to model subsurface flow governed by the modified Helmholtz equation

► We analytically simulate transient groundwater flow with wells and line elements. ► Well and line-element potentials may be evaluated at any distance in Laplace space. ► Heads are computed using a numerical back transformation to the physical domain. ► Line elements are represented either by Mathieu functions or by integrated Bessel functions. ► Applications include flow around impermeable walls and flow to streams in two-aquifer systems.