Logarithmic convexity for discrete harmonic functions and the approximation of the Cauchy problem for Poisson’s equation

Falk, R. S.; Monk, P. B.

doi:10.1090/S0025-5718-1986-0842126-5

Logarithmic convexity for discrete harmonic functions and the approximation of the Cauchy problem for Poisson’s equation
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by R. S. Falk and P. B. Monk PDF

Math. Comp. 47 (1986), 135-149 Request permission

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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