Preconditioning collocation method using quadratic splines with applications to 2^nd-order separable elliptic equations

Abstract

In this paper we propose a P\ finite element preconditioning using the so-called 'hatfunction', to a collocation scheme constructed by quadratic splines for a 2 nd -order separable elliptic operator and we show that the resulting preconditioning system of equations is well conditioned with the condition number independent of the number of unknowns.