This book deals with numerical methods for solving partial differential equa tions (PDEs)
coupling advection, diffusion and reaction terms, with a focus on time-dependency. A …

This book is about adaptive mesh generation and moving mesh methods for the numerical
solution of time-dependent partial differential equations. It presents a general framework and …

Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in
Mechanics and Physics is the first book to provide a systematic construction of exact …

In this article we survey r-adaptive (or moving grid) methods for solving time-dependent
partial differential equations (PDEs). Although these methods have received much less …

In this paper, we present a new method to compute the numerical solution of the elliptic
Monge–Ampère equation. This method is based on solving a parabolic Monge–Ampère …

This article considers a new method for generating a moving mesh which is suitable for the
numerical solution of partial differential equations (PDEs) in several spatial dimensions. The …

A moving mesh finite element algorithm is proposed for the adaptive solution of nonlinear
diffusion equations with moving boundaries in one and two dimensions. The moving mesh …

As more powerful computing hardware enables higher resolution simulations, a fast and
flexible mesh optimization method is becoming increasingly indispensable for …

This article describes a number of velocity-based moving mesh numerical methods for
multidimensional nonlinear time-dependent partial differential equations (PDEs). It consists …

An adaptive moving mesh finite element method is studied for the numerical solution of the
porous medium equation with and without variable exponents and absorption. The method …