Regularization with Differential Operators. II: Weak Least Squares Finite Element Solutions to First Kind Integral Equations

Weak least squares finite element procedures are developed for the numerical solution of first kind integral equations by the method of regularization using differential operators. The representation theory developed in Part I [J. Locker and P. M. Prenter, Regularization with differential operators. I: General theory, J. Math. Anal. Appi., to appear], to which this paper is the sequel, is used to obtain optimal $L^2 $ and $L^\infty $ error estimates together with superconvergence at nodal points for spline approximates to solutions of the associated Euler equation for regularization parameter $\alpha \ne 0$.

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