Optimization of transfinite interpolation of functions with bounded Laplacian by harmonic splines on box partitions

摘要

We consider the problem of optimal transfinite interpolation of functions with the bounded Laplacian by harmonic splines on box-partitions. For anisotropic partitions obtained from the domain of definition by splitting it into equal boxes with the help of parallel hyperplanes, we find asymptotic behaviour of the error of interpolation in terms of the number of boxes in the partition and show that this behaviour does not depend on the number of dimensions. Moreover, we prove that such partition is optimal in at least one particular case. Also, we refine a result on the asymptotic behaviour of the error of adaptive interpolation of twice continuously differentiable functions by harmonic splines. (C) 2016 Elsevier Inc. All rights reserved.