New enrichment strategies for 3D histopolation methods

In this work, we propose a new class of locally enriched histopolation schemes for reconstructing functions defined on three-dimensional domains. Our approach extends standard histopolation techniques by introducing enrichment functions, which significantly enhance accuracy in regions with sharp gradients or intricate geometric structures. We evaluate the performance of the method through a series of numerical experiments, benchmarking it against the classical nonconforming histopolation approach. The results consistently show higher accuracy and faster convergence compared to the classical scheme.