caa a22 4500 445830786 CHVBK 20180317145314.0 cr unu---uuuuu 170323e20110701xx s 000 0 eng 10.1007/s10255-011-0086-6 doi (NATIONALLICENCE)springer-10.1007/s10255-011-0086-6 A two-grid method with expanded mixed element for nonlinear reaction-diffusion equations [Elektronische Daten] [Wei Liu, Hong-xing Rui, Hui Guo] 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. Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg, 2011 two-grid method nationallicence expanded mixed finite element nationallicence reaction-diffusion equation nationallicence nonlinear problem nationallicence Liu Wei School of Mathematics, Shandong University, 250100, Jinan, China aut Rui Hong-xing School of Mathematics, Shandong University, 250100, Jinan, China aut Guo Hui School of Mathematics and Computational Science, China University of Petroleum, 257061, Dongying, China aut Acta Mathematicae Applicatae Sinica, English Series Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 27/3(2011-07-01), 495-502 0168-9673 27:3<495 2011 27 10255 https://doi.org/10.1007/s10255-011-0086-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10255-011-0086-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Liu Wei School of Mathematics, Shandong University, 250100, Jinan, China aut NATIONALLICENCE 700 1- Rui Hong-xing School of Mathematics, Shandong University, 250100, Jinan, China aut NATIONALLICENCE 700 1- Guo Hui School of Mathematics and Computational Science, China University of Petroleum, 257061, Dongying, China aut NATIONALLICENCE 773 0- Acta Mathematicae Applicatae Sinica, English Series Institute of Applied Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 27/3(2011-07-01), 495-502 0168-9673 27:3<495 2011 27 10255 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer