Quadratic B‐spline finite elements are defined for a graded mesh. Hermite infinite elements are proposed to extend the applicability of these finite elements to unbounded regions. Test problems used to compare this technique with published procedures show that the quadratic B‐spline finite element solution has, as expected, lower error bounds than a linear element solution. These experiments also demonstrate that the Hermite infinite elements used to close the B‐spline finite element arrays lead to error norms comparable in size with other infinite element formulations.
The generation of solitary waves in a semi‐infinite shallow channel by boundary forcing is modelled by the Korteweg‐de Vries equation using an array of graded elements closed by a zero pole infinite element. The resulting simulation of solitary wave motion across a non‐uniform mesh confirms existing work and illustrates the effectiveness of the present formulation.