Construction of Basis Functions for the Geometry Conforming Immersed Finite Element Method
Numerical Analysis
2025-10-15 v1 Numerical Analysis
Abstract
The Frenet apparatus is a new framework for constructing high order geometry-conforming immersed finite element functions for interface problems. In this report, we present a procedure for constructing the local IFE bases in some detail as well as a new approach for constructing orthonormal bases using the singular value decomposition of the local generalized Vandermonde matrix. A sample implementation in MATLAB is provided to showcase the simplicity and extensionability of the framework.
Keywords
Cite
@article{arxiv.2510.12018,
title = {Construction of Basis Functions for the Geometry Conforming Immersed Finite Element Method},
author = {Slimane Adjerid and Tao Lin and Haroun Meghaichi},
journal= {arXiv preprint arXiv:2510.12018},
year = {2025}
}