Estimates near plane portions of the boundary for discrete elliptic boundary problems

Author:
C. G. L. Johnson

Journal:
Math. Comp. **28** (1974), 909-935

MSC:
Primary 65N15

DOI:
https://doi.org/10.1090/S0025-5718-1974-0362943-X

MathSciNet review:
0362943

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Abstract: We consider an elliptic difference operator together with certain boundary difference operators near a plane portion of the boundary parallel to some coordinate direction. We prove discrete analogues of known estimates in and Schauder norms for elliptic boundary problems. The discrete estimates are then used to prove results about convergence near plane portions of the boundary of difference quotients of solutions of a discrete elliptic problem to the derivatives of the solution *u* of the corresponding continuous problem, when it is known that converges to *u* in the maximum norm or in a discrete norm as *h* tends to zero.

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1974-0362943-X

Keywords:
Elliptic difference operator,
discrete elliptic boundary problem,
discrete and Schauder estimates,
convergence of difference quotients

Article copyright:
© Copyright 1974
American Mathematical Society