The Deffct Iteration Of The Finite Element And The "Contractity" Of The Interpolatlon Operator For Two-Point Boundary Value Problems

There have been many results about the convergence of iterateddefect correction solutions for finite elements problems ( [1], [2], [3], [4]).In [3-4], the authors have proved that the iterated defect correction oflinear finite element solution for standard elliptic problems converges tothe petrov-Galerkin approximation solution by using the so-calledcontractivity of the interpolation operator for triangular and rectangularelements.Howerer, can we discuss the so-called contractivity of theinterpolation operator for general differential equations? The paperstudied two-point boundary value problems of constant and variablecoefficient in one dimension, especially the singular two-point boundaryvalue problems, and proved the so-called contractivity of linear finiteelement iterated defect correction solutions, and present some numericalexamples. In addition, We also discuss the so-called contractivity betweenlinear and cubic interpolation operator, quadratic and quartic interpolationoperator.