For problems of convection–diffusion type, Eulerian–Lagrangian localized adjoint methods
provide a methodology that maintains the accuracy and efficiency of Eulerian–Lagrangian …

We give a brief summary of numerical methods for time-dependent advection-dominated
partial differential equations (PDEs), including first-order hyperbolic PDEs and nonstationary …

In this work, we present an improvement of the Lagrangian–Eulerian space–time tracking
forward scheme to deal with balance laws and related applications. This extended algorithm …

A contamination source identification problem in constant porous media flow is addressed
by solving the advection–dispersion equation (ADE) with a hierarchical Bayesian …

We design, analyze, and implement an arbitrary-order scheme applicable to generic
meshes for a coupled elliptic-parabolic PDE system describing miscible displacement in …

We present an H1‐Galerkin mixed finite element method for a nonlinear parabolic equation,
which models a compressible fluid flow process in subsurface porous media. The method …

We propose an algorithm for particle tracking based on Cheng's method [Int. J. Numer. Meth.
39 (1996) 1111–1136]. Velocities in a flow field are known at a series of points and …

The release of methane into the working area of coal mines can affect safety and production.
Therefore, methane drainage reduces the risk of explosion and can be used as a fuel and …

Numerical methods and analysis for compressible miscible flow in porous media have been
investigated extensively in the last several decades. Amongst those methods, the lowest …

We prove a priori optimal-order error estimates in a weighted energy norm for several
Eulerian–Lagrangian methods for singularly perturbed, time-dependent convection-diffusion …