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.
All Science Journal Classification (ASJC) codes
- Algebra and Number Theory
- Computational Mathematics
- Applied Mathematics