Stability and regularization for determining sets of discrete Laplacian
Maru Guadie, Eugenia Malinnikova · Inverse Problems · 2013
We study the determining sets for discrete harmonic functions on the square lattices. The stability and regularization of the reconstruction of harmonic functions from its values on a part of a domain are discussed. For some specific configurations, we use the logarithmic convexity estimates to obtain error bounds and propose an optimal choice of the mesh size of discretization.