Frenet-Immersed Finite Elements on Triangular Meshes for Interface Problems
Paper#Numerical Analysis, Finite Element Methods, Interface Problems🔬 Research|Analyzed: Jan 3, 2026 16:10•
Published: Dec 29, 2025 06:37
•1 min read
•ArXivAnalysis
This paper introduces a novel approach to solve elliptic interface problems using geometry-conforming immersed finite element (GC-IFE) spaces on triangular meshes. The key innovation lies in the use of a Frenet-Serret mapping to simplify the interface and allow for exact imposition of jump conditions. The paper extends existing work from rectangular to triangular meshes, offering new construction methods and demonstrating optimal approximation capabilities. This is significant because it provides a more flexible and accurate method for solving problems with complex interfaces, which are common in many scientific and engineering applications.
Key Takeaways
- •Introduces Frenet-IFE spaces on triangular meshes for elliptic interface problems.
- •Uses Frenet-Serret mapping to simplify the interface and impose jump conditions exactly.
- •Provides three construction procedures for high-degree Frenet-IFE spaces.
- •Demonstrates optimal approximation capability.
- •Achieves optimal convergence rates when used with interior penalty discontinuous Galerkin methods.
Reference / Citation
View Original"The paper demonstrates optimal convergence rates in the $H^1$ and $L^2$ norms when incorporating the proposed spaces into interior penalty discontinuous Galerkin methods."