Efficient numerical solution of the dispersion equation using moving finite elements

Abstract

The moving finite element (MFE) method, a moving mesh method, is used to give a highly efficient procedure for numerical solution of the linear, one-dimensional convectioe dispersion equation. For convection dominated dispersion processes it is well known that numerical solution with standard fixed mesh finite elements or finite differences requires large numbers of elements and small time steps in order to satisfy criteria for stability, to give oscillation-free accurate solutions. For such problems numerical solution with fixed mesh methods is consequently inefficient and computationally expensive. In contrast, vie demonstrate here that numerical solutions with highly accurate resolution of steep moving fronts can be generated using the moving finite element method using only a small number of elements and time steps much greater than those afforded by fixed mesh methods.