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), 135-149

MSC:
Primary 65M10; Secondary 35R35, 65M30

DOI:
https://doi.org/10.1090/S0025-5718-1986-0842126-5

MathSciNet review:
842126

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Abstract | References | Similar Articles | Additional Information

Abstract: Logarithmic convexity type continuous dependence results for discrete harmonic functions defined as solutions of the standard piecewise-linear 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:
https://doi.org/10.1090/S0025-5718-1986-0842126-5

Keywords:
Ill-posed problems,
logarithmic convexity,
Poisson's equation

Article copyright:
© Copyright 1986
American Mathematical Society