# 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} }

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…

## 4 Citations

### The lowest-order weak Galerkin finite element method for the Darcy equation on quadrilateral and hybrid meshes

- MathematicsJ. Comput. Phys.
- 2018

### New finite volume element methods in the ALE framework for time-dependent convection-diffusion problems in moving domains

- Computer ScienceJ. Comput. Appl. Math.
- 2021

### Modulus-based Successive Overrelaxation Iteration Method for Pricing American Options with the Two-asset Black–Scholes and Heston's Models Based on Finite Volume Discretization

- Mathematics
- 2021

In this paper we introduce a new numerical method for the linear complementarity problems (LCPs) arising from two-asset Black–Scholes and Heston’s stochastic volatility American options pricing.…

### Construction and analysis of the quadratic finite volume methods on tetrahedral meshes

- Computer ScienceScience China Mathematics
- 2022

Based on the stability, the optimal H 1 and L 2 error estimates respectively are proved, where the orthogonal conditions play an important role in ensuring optimal L 2 convergence rate.

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