Finite Volume Methods (FVM) have become a cornerstone in the numerical treatment of partial differential equations, particularly those governing cross-diffusion and parabolic processes. These ...

Finite volume methods (FVMs) represent a class of numerical techniques that are widely used in the discretisation of elliptic equations, ensuring local conservation of fluxes and often realising high ...

A finite-volume method has been developed that can deal accurately with complicated, curved boundaries for both two-dimensional and three-dimensional axisymmetric advection—diffusion systems. The ...

Mathematical approaches for numerically solving partial differential equations. The focus will be (a) iterative solution methods for linear and non-linear equations, (b) spatial discretization and ...

The conditioning of the linear finite volume element discretization for general diffusion equations is studied on arbitrary simplicial meshes. The condition number is defined as the ratio of the ...