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 …

Objective. Fluorescence molecular tomography (FMT) is a promising non-invasive optical
molecular imaging technology with strong specificity and sensitivity that has great potential …

The Hitchhiker's Guide to the Virtual Element Method | Mathematical Models and Methods in
Applied Sciences World Scientific Search This Journal Anywhere Quick Search in Journals …

The virtual element method (VEM) is a recent technology that can make use of very general
polygonal/polyhedral meshes without the need to integrate complex nonpolynomial …

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 …

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

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 …

We present a method to approximate (in any space dimension) diffusion equations with
schemes having a specific structure; this structure ensures that the discrete local maximum …

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 …