Numerical solution of second-order boundary value problems on nonuniform meshes
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.
- Research Organization:
- National Center for Atmospheric Research, Boulder, CO 80307
- OSTI ID:
- 6228450
- Journal Information:
- Math. Comput.; (United States), Journal Name: Math. Comput.; (United States) Vol. 47:176; ISSN MCMPA
- Country of Publication:
- United States
- Language:
- English
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