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 ...

SIAM Journal on Numerical Analysis, Vol. 54, No. 4 (2016), pp. 2228-2255 (28 pages) We consider the vertex-centered finite volume method with first-order conforming ansatz functions. The adaptive mesh ...

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 ...