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Journal of Scientific Computing

Erschienen in:

01.10.2020

A Novel Arbitrary Lagrangian–Eulerian Finite Element Method for a Mixed Parabolic Problem in a Moving Domain

verfasst von: Rihui Lan, Pengtao Sun

Erschienen in: Journal of Scientific Computing | Ausgabe 1/2020

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Abstract

In this paper, a novel arbitrary Lagrangian–Eulerian (ALE) mapping, thus a novel ALE-mixed finite element method (FEM), is developed and analyzed for a type of mixed parabolic equations in a moving domain. By means of a specific stabilization technique, the mixed finite element of a stable Stokes-pair is utilized to discretize this problem on the ALE description, and, stability and a nearly optimal convergence results are obtained for both semi- and fully discrete ALE finite element approximations. Numerical experiments are carried out to validate all theoretical results. The developed novel ALE–FEM can be also similarly extended to a transient porous (Darcy’s) fluid flow problem in a moving domain as well as to Stokes/Darcy- or Stokes/Biot moving interface problem in the future.

Vorheriger Artikel HDG Methods for Stokes Equation Based on Strong Symmetric Stress Formulations

Nächster Artikel Reconstruction of Quasi-Local Numerical Effective Models from Low-Resolution Measurements

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Titel: A Novel Arbitrary Lagrangian–Eulerian Finite Element Method for a Mixed Parabolic Problem in a Moving Domain
verfasst von: Rihui Lan
Pengtao Sun
Publikationsdatum: 01.10.2020
Verlag: Springer US
Erschienen in: Journal of Scientific Computing / Ausgabe 1/2020
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691
DOI: https://doi.org/10.1007/s10915-020-01315-9

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