Logarithmic Convexity for Discrete Harmonic Functions and the Approximation of the Cauchy Problem for Poisson's Equation
نویسندگان
چکیده
Logarithmic convexity type continuous dependence results for discrete harmonic functions defined as solutions of the standard C" piecewise-linear approximation to Laplace's equation are proved. Using this result, error estimates for a regularizaron method for approximating the Cauchy problem for Poisson's equation on a rectangle are obtained. Numerical results are presented.
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