• DOI:10.1093/IMANUM/DRV029
• Corpus ID: 6314792

Unified analysis of higher-order finite volume methods for parabolic problems on quadrilateral meshes

@article{Yang2016UnifiedAO,
  title={Unified analysis of higher-order finite volume methods for parabolic problems on quadrilateral meshes},
  author={Min Yang and Jiangguo Liu and Qingsong Zou},
  journal={Ima Journal of Numerical Analysis},
  year={2016},
  volume={36},
  pages={872-896}
}

• Min Yang, Jiangguo Liu, Q. Zou
• Published 1 April 2016
• Computer Science
• Ima Journal of Numerical Analysis

Finite volume methods (FVMs) have been widely used in scientific computing and engineering due to their easy implementation and the local conservation property. Lower-order FVMs are tightly related to finite difference or finite element methods, and have been extensively studied for a long time; see, e.g., Angelini et al. (2013), Bank & Rose (1987), Chatzipantelidis et al. (2008), Chou & Ye (2007), Ewing et al. (2002), Eymard et al. (2000), Hackbusch (1989), Hajibeygi & Jenny (2009) and Li et al. (2000). Compared with lower-order methods, higher-order FVMs can produce more accurate solutions, and have been widely used in computational fluid dynamics to effectively resolve complex-flow features; see, e.g., Castro et al. (2006), Colella et al. (2011) and Zhang & Phillip (2012). However, the progress on the theoretical analysis of higher-order FVMs is rather slow. Over the last few years, research on higher-order FVMs mainly focused on elliptic problems. The difficulty for the analysis lies in the establishment of stability (or inf–sup condition in general). Some earlier works in Li et al. (2000), Liebau (1996), Xu & Zou (2009), Lv & Li (2012) and Chen et al. (2012) adopt the so-called elementwise stiffness matrix analysis, which estimates the eigenvalues of the local stiffness matrix, and thus has to be proceeded scheme by scheme. To the best of our knowledge, only a few systematic works on high-order finite volume scheme appeared in the literature. For instance, a