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Mathematics of Computation

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Uniform expansions for a class of finite difference schemes for elliptic boundary value problems


Author: Harry Munz
Journal: Math. Comp. 36 (1981), 155-170
MSC: Primary 65N05
DOI: https://doi.org/10.1090/S0025-5718-1981-0595048-7
MathSciNet review: 595048
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Abstract: For a class of finite difference schemes for the Dirichlet problem on a bounded region $ \Omega \subset {{\mathbf{R}}^n}$, the existence of uniform expansions of the approximate solution for meshlength $ h \to 0$ is shown. The results also improve error bounds which Pereyra, Proskurowski, and Widlund obtained with respect to certain discrete $ {L_2}$-norms.


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DOI: https://doi.org/10.1090/S0025-5718-1981-0595048-7
Article copyright: © Copyright 1981 American Mathematical Society