DISCRETE CLOSURE AND ASYMPTOTIC (QUASI-) REGULARITY IN DISCRETIZATION ALGORITHMS
P. M. Anselone, R. Ansorge · IMA Journal of Numerical Analysis · 1987
This paper is concerned with general principles that underlie approximation methods in numerical analysis, particularly difference methods for differential equations. We seek minimal conditions that imply the convergence of approximate solutions, independent of existence and uniqueness. Central roles are played by closure and regularity properties of the operators involved.