HERMITE INFINITE ELEMENTS AND GRADED QUADRATIC B-SPLINE FINITE-ELEMENTS

Quadratic B-spline finite elements are defined for a graded mesh. Herm ite infinite elements are proposed to extend the applicability of thes e finite elements to unbounded regions. Test problems used to compare this technique with published procedures show that the quadratic B-spl ine 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 a rrays lead to error norms comparable in size with other infinite eleme nt formulations. The generation of solitary waves in a semi-infinite s hallow channel by boundary forcing is modelled by the Korteweg-de Vrie s equation using an array of graded elements closed by a zero pole inf inite element. The resulting simulation of solitary wave motion across a non-uniform mesh confirms existing work and illustrates the effecti veness of the present formulation.