Finite volume methods are a class of discretization schemes resulting from the
decomposition of a problem domain into nonoverlapping control volumes. Degrees of …

We consider nonlinear algebraic systems resulting from numerical discretizations of
nonlinear partial differential equations of diffusion type. To solve these systems, some …

Recently, engineers, scientists, and mathematicians have concentrated their efforts on
numerical methods for solving the Navier–Stokes equations. The reason is that these …

In this paper, for the first time we propose two linear, decoupled, energy-stable numerical
schemes for multicomponent two-phase compressible flow with a realistic equation of state …

In this work, we consider the transport of a surfactant in variably saturated porous media.
The water flow is modelled by the Richards equations and it is fully coupled with the …

Two research subjects in geosciences which lately underwent significant progress are
treated in this review. In the first part, we focus on one key ingredient for the numerical …

In this work, we present a mass conservative numerical scheme for two-phase flow in porous
media. The model for flow consists of two fully coupled, nonlinear equations: a degenerate …

This paper is concerned with the numerical simulation of time-dependent variably-saturated
Darcian flow problems described by the Richards equation. We present the adaptive higher …

This paper develops a general abstract framework for a posteriori estimates for immiscible
incompressible two-phase flows in porous media. We measure the error by the dual norm of …

We consider a second-order elliptic boundary value problem with strongly monotone and
Lipschitz-continuous nonlinearity. We design and study its adaptive numerical …