A high-order selective DG method with a new hybrid IFE space is introduced for elliptic interface problems on unfitted meshes, with proofs of optimal approximation, well-posedness, and a priori error estimates in energy and L2 norms.
arXiv preprint arXiv:2510.12018 (2025)
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Introduces three high-order Frenet-IFE constructions on triangular meshes that achieve optimal H1 and L2 convergence when used in interior penalty discontinuous Galerkin methods for elliptic interface problems.
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A Priori Error Analysis of a High-Order Selective Discontinuous Galerkin Method for Elliptic Interface Problems
A high-order selective DG method with a new hybrid IFE space is introduced for elliptic interface problems on unfitted meshes, with proofs of optimal approximation, well-posedness, and a priori error estimates in energy and L2 norms.
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Frenet Immersed Finite Element Spaces on Triangular Meshes
Introduces three high-order Frenet-IFE constructions on triangular meshes that achieve optimal H1 and L2 convergence when used in interior penalty discontinuous Galerkin methods for elliptic interface problems.