## An adaptive method of lines with error control for parabolic equations of the reaction-diffusion type.(English)Zbl 0596.65084

Authors’ summary: 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 vertical 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 and is implemented in the program FEMOL 1, which uses the LSODI package 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.
Reviewer: P.Laasonen

### MSC:

 65N40 Method of lines for boundary value problems involving PDEs 65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs 65N15 Error bounds for boundary value problems involving PDEs 35K60 Nonlinear initial, boundary and initial-boundary value problems for linear parabolic equations
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### References:

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