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 develop new stabilized mixed finite element methods for Darcy flow. Stability and an a
priori error estimate in the “stability norm” are established. A wide variety of convergent finite …

A recently introduced theory of solute transport in porous media is tested by comparison with
experiment. The solute transport is predicted using an adaptation of the cluster statistics of …

In this work, we construct and analyze a new fully discrete Lagrangian-Eulerian numerical
method for the treatment of dynamics of conservation laws with nonlocal flux and influence …

In this work, we develop an improved shock-capturing and high-resolution Lagrangian–
Eulerian method for hyperbolic systems and balance laws. This is a new method to deal with …

In this work, we design a new class of fully discrete Lagrangian–Eulerian schemes on
triangular grids to approximate nonlinear multidimensional initial value problems for scalar …

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 …

We develop a new finite volume scheme for numerically solving transport models associated
with hyperbolic problems and balance laws. The numerical scheme is obtained via a …

We develop a locally conservative Eulerian–Lagrangian finite volume scheme with the
weighted essentially non-oscillatory property (EL–WENO) in one-space dimension. This …

In this work, we introduce a new semi-discrete scheme based on the so-called no-flow
curves and its numerical analysis for solving initial value problems that involve one …