We present Finite Volume methods for diffusion equations on generic meshes, that received
important coverage in the last decade or so. After introducing the main ideas and …

This book provides a self-contained introduction to the simulation of flow and transport in
porous media, written by a developer of numerical methods. The reader will learn how to …

This book describes the theoretical and computational aspects of the mimetic finite
difference method for a wide class of multidimensional elliptic problems, which includes …

We propose a discretization‐free approach based on the physics‐informed neural network
(PINN) method for solving the coupled advection‐dispersion equation (ADE) and Darcy flow …

We construct a nonlinear finite volume (FV) scheme for diffusion equation on star-shaped
polygonal meshes and prove that the scheme is monotone, ie, it preserves positivity of …

We developed a new monotone finite volume method for diffusion equations. The second-
order linear methods, such as the multipoint flux approximation, mixed finite element and …

This chapter is concerned with the design of high-resolution finite element schemes
satisfying the discrete maximum principle. The presented algebraic flux correction paradigm …

We present two new cell-centered nonlinear finite-volume methods for the heterogeneous,
anisotropic diffusion problem. The schemes split the interfacial flux into harmonic and …

Steel corrosion plays an adversary, but central role in different technological fields.
Reasonable modeling of corrosion calls for a profound theoretical study of the underlying …

We present a new second-order accurate monotone finite volume (FV) method for the steady-
state advection–diffusion equation. The method uses a nonlinear approximation for both …