Optimal convergence analysis of arbitrary Lagrangian-Eulerian finite element methods for two-phase Stokes flow problems with moving interface
Abstract
In this paper, an arbitrary Lagrangian-Eulerian (ALE)-based finite element method (FEM) is developed and studied in a monolithic framework for a class of two-phase Stokes flow problems with moving interfaces and jump coefficients, where the mixed finite element approximation to Stokes moving interface problems is established and analyzed in both semi- and fully discrete schemes based on the ALE formulation. The key analytical technique involves a specific H^1-projection associated with the ALE-induced mesh motion due to the evolving interface. Optimal convergence properties of the proposed H^1-projection and its ALE temporal derivative are proved in both H^1 and L^2 norms, with which optimal error estimates are obtained for both semi- and fully discrete mixed finite element approximations to the studied Stokes moving interface problem in both H1 and L2 norms as well. Numerical experiments are carried out to validate all derived theoretical results. The developed analytical approach can be extended to Taylor-Hood and MINI mixed elements, as well as to more general two-phase flow problems.
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BibTeX
@misc{liang2026optimal,
title = {{Optimal convergence analysis of arbitrary Lagrangian-Eulerian finite element methods for two-phase Stokes flow problems with moving interface}},
author = {Yi Liang and Cheng Wang and Pengtao Sun and Yan Chen and Jiarui Han},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.32066},
eprint = {2609.32066},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.32066},
}
RIS
TY - UNPB
TI - Optimal convergence analysis of arbitrary Lagrangian-Eulerian finite element methods for two-phase Stokes flow problems with moving interface
AU - Yi Liang
AU - Cheng Wang
AU - Pengtao Sun
AU - Yan Chen
AU - Jiarui Han
PY - 2026
DA - 2026/09/25
PB - arXiv
DO - 10.48550/arxiv.2609.32066
UR - https://arxiv.org/abs/2609.32066
AB - In this paper, an arbitrary Lagrangian-Eulerian (ALE)-based finite element method (FEM) is developed and studied in a monolithic framework for a class of two-phase Stokes flow problems with moving interfaces and jump coefficients, where the mixed finite element approximation to Stokes moving interface problems is established and analyzed in both semi- and fully discrete schemes based on the ALE formulation. The key analytical technique involves a specific H^1-projection associated with the ALE-induced mesh motion due to the evolving interface. Optimal convergence properties of the proposed H^1-projection and its ALE temporal derivative are proved in both H^1 and L^2 norms, with which optimal error estimates are obtained for both semi- and fully discrete mixed finite element approximations to the studied Stokes moving interface problem in both H1 and L2 norms as well. Numerical experiments are carried out to validate all derived theoretical results. The developed analytical approach can be extended to Taylor-Hood and MINI mixed elements, as well as to more general two-phase flow problems.
ER -