# A face-centred finite volume method for second-order elliptic problems

@article{Sevilla2017AFF, title={A face-centred finite volume method for second-order elliptic problems}, author={Rub{\'e}n Sevilla and Matteo Giacomini and Antonio Huerta}, journal={ArXiv}, year={2017}, volume={abs/1712.06173} }

This work proposes a novel finite volume paradigm, the face-centred finite volume (FCFV) method. Contrary to the popular vertex (VCFV) and cell (CCFV) centred finite volume methods, the novel FCFV defines the solution on the mesh faces (edges in 2D) to construct locally-conservative numerical schemes.
The idea of the FCFV method stems from a hybridisable discontinuous Galerkin (HDG) formulation with constant degree of approximation, thus inheriting the convergence properties of the classical…

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## 16 Citations

A second-order face-centred finite volume method for elliptic problems

- Mathematics, Computer ScienceArXiv
- 2019

The proposed FCFV method is based on a mixed formulation and therefore considers the solution and its gradient as independent unknowns, which leads to a method that is insensitive to mesh distortion and stretching and its potential in three dimensional problems with complex geometries.

A locking-free face-centred finite volume (FCFV) method for linear elasticity

- Mathematics, Computer ScienceArXiv
- 2019

A face-centred finite volume (FCFV) method is proposed for the linear elasticity equation. The FCFV is a mixed hybrid formulation, featuring a system of first-order equations, that defines the…

A locking-free face-centred finite volume (FCFV) method for linear elastostatics

- Physics, MathematicsComputers & Structures
- 2019

Abstract A face-centred finite volume (FCFV) method is proposed for linear elastostatic problems. The FCFV is a mixed hybrid formulation, featuring a system of first-order equations, that defines the…

A coupled HDG-FV scheme for the simulation of transient inviscid compressible flows

- Computer Science
- 2020

Abstract A methodology that combines the advantages of the vertex-centred finite volume (FV) method and high-order hybridisable discontinuous Galerkin (HDG) method is presented for the simulation of…

Discontinuous Galerkin approximations in computational mechanics: hybridization, exact geometry and degree adaptivity

- Computer Science, MathematicsSN Applied Sciences
- 2019

Applications involving the numerical simulation of problems in electrostatics, linear elasticity and incompressible viscous flows, and the hybridizable discontinuous Galerkin (HDG) method are presented.

HDG-NEFEM for two dimensional linear elasticity

- MathematicsComputers & Structures
- 2019

Abstract This paper proposes a new methodology for the solution of two dimensional linear elastic problems in domains with curved boundaries. The proposed method exploits the advantages of the…

Proper generalized decomposition for parameterized elliptic PDE’s

- 2018

The computational cost of parametric studies currently represents the major limitation to the application of simulation-based engineering techniques in a daily industrial environment. Parameters of…

Nonintrusive proper generalised decomposition for parametrised incompressible flow problems in OpenFOAM

- Computer Science, MathematicsComput. Phys. Commun.
- 2020

This work presents the first nonintrusive implementation of the proper generalised decomposition (PGD) in OpenFOAM, for the approximation of parametrised laminar incompressible Navier-Stokes equations.

Thirty Years of the Finite Volume Method for Solid Mechanics

- Computer Science, Mathematics
- 2018

An overview, historical perspective, comparison and critical analysis of the different approaches, including their relative strengths, weaknesses, similarities and dissimilarities, where a close comparison with the de facto standard for computational solid mechanics, the finite element method is given.

Workshop: Computational Engineering Table of Contents

- 2016

This Workshop treated a variety of finite element methods and applications in computational engineering and expanded their mathematical foundation in engineering analysis. Among the 53 participants…

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