Mathematics of Computation

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Convergence estimates for essentially positive type discrete Dirichlet problems

Authors: J. H. Bramble, B. E. Hubbard and Vidar Thomée
Journal: Math. Comp. 23 (1969), 695-709
MSC: Primary 65.66
MathSciNet review: 0266444
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Abstract: In this paper we consider a class of difference approximations to the Dirichlet problem for second-order elliptic operators with smooth coefficients. The main result is that if the order of accuracy of the approximate problem is $ \mathcal{V}$, and $ F$ (the right-hand side) and $ f$ (the boundary values) both belong to $ {C^\lambda }$ for $ \lambda < \mathcal{V}$, then the rate of convergence is $ O({h^\lambda })$.

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Article copyright: © Copyright 1969 American Mathematical Society