Estimates near plane portions of the boundary for discrete elliptic boundary problems
Author:
C. G. L. Johnson
Journal:
Math. Comp. 28 (1974), 909935
MSC:
Primary 65N15
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:
http://dx.doi.org/10.1090/S0025571819740362943X
PII:
S 00255718(1974)0362943X
Keywords:
Elliptic difference operator,
discrete elliptic boundary problem,
discrete and Schauder estimates,
convergence of difference quotients
Article copyright:
© Copyright 1974
American Mathematical Society
