Logarithmic convexity for discrete harmonic functions and the approximation of the cauchy problem for poisson's equation

R. S. Falk, P. B. Monk

Research output: Contribution to journalArticlepeer-review

51 Scopus citations

Abstract

Logarithmic convexity type continuous dependence results for discrete harmonic functions defined as solutions of the standard C0 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.

Original languageEnglish (US)
Pages (from-to)135-149
Number of pages15
JournalMathematics of Computation
Volume47
Issue number175
DOIs
StatePublished - Jul 1986

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory
  • Computational Mathematics
  • Applied Mathematics

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