This report demonstrates a new approach for constructing orthonormal bases in geometry-conforming immersed finite elements, highlighting applications in interface problems.
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.
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Adjerid et al. (2025) studied this question.
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