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

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 …

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

We develop an Eulerian--Lagrangian localized adjoint method (ELLAM)-mixed finite
element method (MFEM) solution technique for accurate numerical simulation of coupled …

We develop a family of Eulerian–Lagrangian localized adjoint methods for the solution of the
initial-boundary value problems for first-order advection-reaction equations on general multi …

This work represents the essence of nearly 16 years of work in scientific computing for
ocean and atmospheric modeling. This journey started at Alfred-Wegener-Institute for Polar …

This is the second of a sequence of papers devoted to applying the localized adjoint method
(LAM), in space‐time, to problems of advective‐diffusive transport. We refer to the resulting …

Eulerian-Lagrangian localized adjoint methods (ELLAM) are developed for the nonlinear
Buckley-Leverett equation, which is characterized by degenerate diffusion and sharpening …