The numerical solution of second-order boundary value problems on nonuniform meshes

Authors:
Thomas A. Manteuffel and Andrew B. White

Journal:
Math. Comp. **47** (1986), 511-535, S53

MSC:
Primary 65L10

DOI:
https://doi.org/10.1090/S0025-5718-1986-0856700-3

MathSciNet review:
856700

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper, we examine the solution of second-order, scalar boundary value problems on nonuniform meshes. We show that certain commonly used difference schemes yield second-order accurate solutions despite the fact that their truncation error is of lower order. This result illuminates a limitation of the standard stability, consistency proof of convergence for difference schemes defined on nonuniform meshes. A technique of reducing centered-difference approximations of first-order systems to discretizations of the underlying scalar equation is developed. We treat both vertex-centered and cell-centered difference schemes and indicate how these results apply to partial differential equations on Cartesian product grids.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1986-0856700-3

Keywords:
Boundary value problems,
compact difference schemes,
irregular grids,
nonuniform mesh,
difference quotients,
truncation error

Article copyright:
© Copyright 1986
American Mathematical Society