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A Mesh-Independence Principle for Operator Equations and Their Discretizations
E. L. Allgower, K. Bohmer, F. A. Potra and W. C. Rheinboldt
SIAM Journal on Numerical Analysis
Vol. 23, No. 1 (Feb., 1986), pp. 160-169
Published by: Society for Industrial and Applied Mathematics
Stable URL: http://www.jstor.org/stable/2157457
Page Count: 10
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The mesh-independence principle asserts that, when Newton's method is applied to a nonlinear equation between some Banach spaces as well as to some finite-dimensional discretization of that equation, then the behavior of the discretized process is asymptotically the same as that for the original iteration and, as a consequence, the number of steps required by the two processes to converge to within a given tolerance is essentially the same. So far this result has been proved only for certain classes of boundary value problems. In this paper a proof is presented for a general class of operator equations and discretizations. It covers the earlier results and extends them well beyond the cases that have been considered before.
SIAM Journal on Numerical Analysis © 1986 Society for Industrial and Applied Mathematics