On the Choice of Continuous and Discontinuous Lagrange Multipliers in Fictitious-Domain Methods
Abstract
This article examines the Fictitious-Domain approach using Distributed Lagrange Multipliers (FD-DLM), a method that handles elliptic interface problems with separate meshes without requiring the interface to match the background mesh. It compares two stable, low-order FD-DLM discretizations when using both continuous and discontinuous multiplier spaces. The study distinguishes between satisfying the weak coupling constraint per element and the size of the discrepancy between the two discrete primal fields. Numerical experiments indicate that the continuous formulation usually yields smaller local errors and maximum mismatch values, while the discontinuous formulation shows a more regular decrease in mismatch as the mesh is refined and has smaller primal errors.
Related
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BibTeX
@misc{alshehri2026choice,
title = {{On the Choice of Continuous and Discontinuous Lagrange Multipliers in Fictitious-Domain Methods}},
author = {Najwa Alshehri and Shumoua F. Alrzqi},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.03267},
eprint = {2610.03267},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.03267},
}
RIS
TY - UNPB
TI - On the Choice of Continuous and Discontinuous Lagrange Multipliers in Fictitious-Domain Methods
AU - Najwa Alshehri
AU - Shumoua F. Alrzqi
PY - 2026
DA - 2026/10/02
PB - arXiv
DO - 10.48550/arxiv.2610.03267
UR - https://arxiv.org/abs/2610.03267
AB - This article examines the Fictitious-Domain approach using Distributed Lagrange Multipliers (FD-DLM), a method that handles elliptic interface problems with separate meshes without requiring the interface to match the background mesh. It compares two stable, low-order FD-DLM discretizations when using both continuous and discontinuous multiplier spaces. The study distinguishes between satisfying the weak coupling constraint per element and the size of the discrepancy between the two discrete primal fields. Numerical experiments indicate that the continuous formulation usually yields smaller local errors and maximum mismatch values, while the discontinuous formulation shows a more regular decrease in mismatch as the mesh is refined and has smaller primal errors.
ER -