Abstract
Expanded mixed finite element approximation of nonlinear reaction-diffusion equations is discussed. The equations considered here are used to model the hydrologic and bio-geochemical phenomena. To linearize the mixed-method equations, we use a two-grid method involving a small nonlinear system on a coarse gird of size H and a linear system on a fine grid of size h. Error estimates are derived which demonstrate that the error is O(Δt + h k+1 + H 2k+2−d/2) (k ≥ 1), where k is the degree of the approximating space for the primary variable and d is the spatial dimension. The above estimates are useful for determining an appropriate H for the coarse grid problems.
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Supported by the National Natural Science Foundation of China Grant (No. 10771124); the Research Fund for Doctoral Program of High Education by State Education Ministry of China (No. 20060422006); the Program for Innovative Research Team in Ludong University; the Discipline Construction Fund of Ludong University.
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Liu, W., Rui, Hx. & Guo, H. A two-grid method with expanded mixed element for nonlinear reaction-diffusion equations. Acta Math. Appl. Sin. Engl. Ser. 27, 495–502 (2011). https://doi.org/10.1007/s10255-011-0086-6
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DOI: https://doi.org/10.1007/s10255-011-0086-6