A two-grid method with expanded mixed element for nonlinear reaction-diffusion equations

作者：Liu, Wei^*; Rui, Hong-xing; Guo, Hui

来源：Acta Mathematicae Applicatae Sinica-English Series, 2011, 27(3): 495-502.

DOI：10.1007/s10255-011-0086-6

• two-grid method
• expanded mixed finite element
• reaction-diffusion equation
• nonlinear problem

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(Delta t + h (k+1) + H (2k+2-d/2)) (k a parts per thousand yen 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.

• 出版日期2011-7
• 单位鲁东大学; 中国石油大学（北京）; 山东大学