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

Abstract

AbstractIn this paper we propose a P1 finite element preconditioning using the so-called ‘hat-function’, to a collocation scheme constructed by quadratic splines for a 2nd-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.