Immersed finite element methods for convection diffusion equationsopen access
- Authors
- Jo, Gwanghyun; Kwak, Do Y.
- Issue Date
- Jan-2023
- Publisher
- PO BOX 2604, SPRINGFIELD, USA, MO, 65801-2604
- Keywords
- control volume; convection-diffusion problem; immersed finite element method; interface problem; upwinding scheme
- Citation
- AIMS Mathematics, v.8, no.4, pp 8034 - 8059
- Pages
- 26
- Indexed
- SCIE
SCOPUS
- Journal Title
- AIMS Mathematics
- Volume
- 8
- Number
- 4
- Start Page
- 8034
- End Page
- 8059
- URI
- https://scholarworks.bwise.kr/erica/handle/2021.sw.erica/115210
- DOI
- 10.3934/math.2023407
- ISSN
- 2473-6988
- Abstract
- In this work, we develop two IFEMs for convection-diffusion equations with interfaces. We first define bilinear forms by adding judiciously defined convection-related line integrals. By establishing Gårding’s inequality, we prove the optimal error estimates both in L2 and H1-norms. The second method is devoted to the convection-dominated case, where test functions are piecewise constant functions on vertex-associated control volumes. We accompany the so-called upwinding concepts to make the control-volume based IFEM robust to the magnitude of convection terms. The H1 optimal error estimate is proven for control-volume based IFEM. We document numerical experiments which confirm the analysis. © 2023 the Author(s), licensee AIMS Press.
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