An FDM-sFEM scheme on time-space manifolds and its superconvergence analysis
Abstract
We study superconvergent discretization of the Laplace-Beltrami operator on time-space product manifolds with Neumann temporal boundary values, which arise in the context of dynamic optimal transport on general surfaces. We propose a coupled scheme that combines finite difference methods in time with surface finite element methods in space. By establishing a new summation by parts formula and proving the supercloseness of the semi-discrete solution, we derive superconvergence results for the recovered gradient via post-processing techniques. In addition, our geometric error analysis is implemented within a novel framework based on the approximation of the Riemannian metric. Several numerical examples are provided to validate and illustrate the theoretical results.
Keywords
Cite
@article{arxiv.2507.17378,
title = {An FDM-sFEM scheme on time-space manifolds and its superconvergence analysis},
author = {Chengrun Jiang and Guozhi Dong and Hailong Guo and Zuoqiang Shi},
journal= {arXiv preprint arXiv:2507.17378},
year = {2025}
}