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

by   Luan M Vieira, et al.

A second-order face-centred finite volume method (FCFV) is proposed. Contrary to the more popular cell-centred and vertex-centred finite volume (FV) techniques, the proposed method defines the solution on the faces of the mesh (edges in two dimensions). The method is based on a mixed formulation and therefore considers the solution and its gradient as independent unknowns. They are computed solving an element-by-element problem after the solution at the faces is determined. The proposed approach avoids the need of reconstructing the solution gradient, as required by cell-centred and vertex-centred FV methods. This strategy leads to a method that is insensitive to mesh distortion and stretching. The current method is second-order and requires the solution of a global system of equations of identical size and identical number of non-zero elements when compared to the recently proposed first-order FCFV. The formulation is presented for Poisson and Stokes problems. Numerical examples are used to illustrate the approximation properties of the method as well as to demonstrate its potential in three dimensional problems with complex geometries. The integration of a mesh adaptive procedure in the FCFV solution algorithm is also presented.


page 21

page 23

page 24

page 26

page 27


A second-order face-centred finite volume method on general meshes with automatic mesh adaptation

A second-order face-centred finite volume strategy on general meshes is ...

Adaptive geometric multigrid for the mixed finite cell formulation of Stokes and Navier-Stokes equations

Unfitted finite element methods have emerged as a popular alternative to...

Least-Squares Methods with Nonconforming Finite Elements for General Second-Order Elliptic Equations

In this paper, we study least-squares finite element methods (LSFEM) for...

On the numerical accuracy in finite-volume methods to accurately capture turbulence in compressible flows

The goal of the present paper is to understand the impact of numerical s...

A Complex-boundary Treatment Method for Finite Volume Schemes with Cut-Cartesian Cell Mesh

In this paper, a second-order accurate method was developed for calculat...

Multicontinuum homogenization. General theory and applications

In this paper, we discuss a general framework for multicontinuum homogen...

A cell-centred finite volume formulation of geometrically-exact Simo-Reissner beams with arbitrary initial curvatures

This paper presents a novel total Lagrangian cell-centred finite volume ...

Please sign up or login with your details

Forgot password? Click here to reset