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 …

Fractures form the main pathways for flow in the subsurface within low-permeability rock. For
this reason, accurately predicting flow and transport in fractured systems is vital for …

This book presents a systematic methodology for the development of parallel multi-physics
models and its implementation in geophysical and biomedical applications. The …

We construct a new nonlinear finite volume scheme for diffusion equation on polygonal
meshes and prove that the scheme satisfies the discrete extremum principle. Our scheme is …

We present a numerical method for approximating the solutions of degenerate parabolic
equations with a formal gradient flow structure. The numerical method we propose …

We propose a cell-centered finite volume (FV) scheme with the minimal stencil formed by the
closest neighbouring cells. The discrete solution satisfies the discrete maximum principle …

We present a new nonlinear monotone finite volume method for diffusion equation and its
application to two-phase flow model. We consider full anisotropic discontinuous diffusion or …

Platelets upregulate the generation of thrombin and reinforce the fibrin clot which increases
the incidence risk of venous thromboembolism (VTE). However, the role of platelets in the …

The maximum principle is one of the most important properties of solutions of partial
differential equations. Its numerical analog, the discrete maximum principle (DMP), is one of …

We present in this article a positive finite volume method for diffusion equation on deformed
meshes. This method is mainly inspired from, and uses auxiliary unknowns at the nodes of …