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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: Logarithmic convexity type continuous dependence results for discrete harmonic functions defined as solutions of the standard $ {C^0}$ 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

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