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

Manteuffel, Thomas A.; White, Andrew B.

doi:10.1090/S0025-5718-1986-0856700-3

The numerical solution of second-order boundary value problems on nonuniform meshes
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by Thomas A. Manteuffel and Andrew B. White PDF

Math. Comp. 47 (1986), 511-535 Request permission

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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