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

The analysis of singular perturbed differential equations began early in the twentieth
century, when approximate solutions were constructed from asymptotic expansions …

During recent years the authors and collaborators have been involved in an activity related
to the construction and analysis of large time step operator splitting algorithms for the …

Two decades ago when we wrote Spectral Methods in Fluid Dynamics (1988), the subject
was still fairly novel. Motivated by the many favorable comments we have received and the …

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

Models of two phase flows in porous media, used in petroleum engineering, lead to a
system of two coupled equations with elliptic and parabolic degenerate terms, and two …

This article discusses a bilinear immersed finite element (IFE) space for solving second‐
order elliptic boundary value problems with discontinuous coefficients (interface problem) …

We develop an Eulerian--Lagrangian localized adjoint method (ELLAM) to solve two-
dimensional advection-diffusion equations with all combinations of inflow and outflow …

The method of characteristics type is especially effective for convection-dominated diffusion
problems. Due to the nature of characteristic temporal discretization, the method allows one …

The mammalian liver plays a key role for metabolism and detoxification of xenobiotics in the
body. The corresponding biochemical processes are typically subject to spatial variations at …