Multiscale methods based on coupled partial differential equations defined on bulk and
embedded manifolds are still poorly explored from the theoretical standpoint, although they …

Core Ideas We present a locally mass‐conservative flow, transport, and root–soil interaction
model. We include a sustainable, flexible research software framework for plant‐scale …

Many biological and geological systems can be modeled as porous media with small
inclusions. Vascularized tissue, roots embedded in soil or fractured rocks are examples of …

Coupled partial differential equations (PDEs) defined on domains with different
dimensionality are usually called mixed-dimensional PDEs. We address mixed-dimensional …

A large variety of severe medical conditions involve alterations in microvascular circulation.
Hence, measurements or simulation of circulation and perfusion has considerable clinical …

We present a two‐phase model for microcirculation that describes the interaction of plasma
with red blood cells. The model takes into account of typical effects characterizing the …

In this paper, we study the mathematical structure and numerical approximation of elliptic
problems posed in a (3D) domain Ω when the right-hand side is a (1D) line source Λ. The …

We develop a mathematical model for the interaction of a three-dimensional reservoir with
the flow through wells, namely narrow cylindrical channels cutting across the reservoir. Leak …

In this work, we develop an efficient solver based on neural networks for second-order
elliptic equations with variable coefficients and a singular source. This class of problems …

Finite element methods have been shown to achieve high accuracies in numerically solving
the EEG forward problem and they enable the realistic modeling of complex geometries and …