Author(s)

Li Wu, Myron B. Allen and Eun-Jae Park

Abstract

We present a method for solving nonlinear reaction-diffusion equations, s^-V ot using a mixed finite-element method. To linearize the mixed-method equa- tions, we use a two-grid scheme that relegates all of the Newton-like iter- ations to grids much coarser than the original one, with no loss in order of accuracy. The use of a multigrid-based solver for the indefinite linear systems that arise at each iteration, as well as for the similar system that arises on the fine grid, allows for even greater efficiency. 1 Introduction Reaction-diffusion equations occur in several hydrologic applications, including mathematical models of leaky aquifers [7] and biogeochem- ical phenomena [5]. Equations of the form /(x,p) (1)

Keywords