An adaptive method of lines with error control for parabolic equations of the reaction-diffusion type

Abstract A piecewise linear finite element-based method of lines is presented for the numerical solution of coupled parabolic partial differential equations which model biological and physicochemical reaction-diffusion processes in one space dimension. The vertial lines emanating from the space nodes in this method change at automatically selected times when, in order to control a norm of the space discretization error, adaptive spatial regridding occurs. The regridding algorithm is an extension of one described previously by the authors [7] and is implemented in the program FEMOL 1, which uses the LSODI package [14, 15] of Hindmarsh and Painter to integrate the ordinary differential equations in time along the vertical lines. Computational results show that the method is efficient, that a posteriori estimates of the space discretization error are accurate, and that the adaptive procedure reliably controls the space discretization error.