Abstract
AbstractThe upwinded finite element method was introduced for the solution of conduction–convection problems by considering the model problem, u″‐Ku′=0, K>0, subject to the boundary conditions u(0)=1, u(1)=0. In this paper we consider the solution of this problem by the collocation method using piecewise cubic Hermite polynomials and a uniform grid. We consider the collocation points to be arbitrary parameters which enable us to express the collocation points in terms of the upwinding parameter of the upwinded finite element method. Various choices of the collocation points, including values which lead to complete accuracy in the nodal function values as well as the nodal values of the derivatives are discussed. Finally, we discuss the application of these points to slightly more general problems. Numerical results illustrating the behaviour of these points are given.
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