Logarithmic convexity for discrete harmonic functions and the approximation of the Cauchy problem for Poisson's equation
Authors:
R. S. Falk and P. B. Monk
Journal:
Math. Comp. 47 (1986), 135149
MSC:
Primary 65M10; Secondary 35R35, 65M30
MathSciNet review:
842126
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Abstract: Logarithmic convexity type continuous dependence results for discrete harmonic functions defined as solutions of the standard piecewiselinear approximation to Laplace's equation are proved. Using this result, error estimates for a regularization method for approximating the Cauchy problem for Poisson's equation on a rectangle are obtained. Numerical results are presented.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718198608421265
PII:
S 00255718(1986)08421265
Keywords:
Illposed problems,
logarithmic convexity,
Poisson's equation
Article copyright:
© Copyright 1986
American Mathematical Society
