Convergence of an adaptive mixed finite element method for convection-diffusion-reaction equations  

作　　者：DU ShaoHong XIE XiaoPing 

机构地区：[1]School of Science, Chongqing Jiaotong University [2]Beijing Computational Science Research Center [3]School of Mathematics, Sichuan University

出　　处：《Science China Mathematics》2015年第6期1327-1348,共22页中国科学：数学（英文版）

基　　金：supported by Education Science Foundation of Chongqing(Grant No.KJ120420);National Natural Science Foundation of China(Grant No.11171239);Major Research Plan of National Natural Science Foundation of China(Grant No.91430105);Open Fund of Key Laboratory of Mountain Hazards and Earth Surface Processes,Chinese Academy Sciences

摘　　要：We prove the convergence of an adaptive mixed finite element method(AMFEM) for(nonsymmetric) convection-diffusion-reaction equations. The convergence result holds for the cases where convection or reaction is not present in convection- or reaction-dominated problems. A novel technique of analysis is developed by using the superconvergence of the scalar displacement variable instead of the quasi-orthogonality for the stress and displacement variables, and without marking the oscillation dependent on discrete solutions and data. We show that AMFEM is a contraction of the error of the stress and displacement variables plus some quantity. Numerical experiments confirm the theoretical results.We prove the convergence of an adaptive mixed finite element method（AMFEM） for（nonsymmetric） convection-diffusion-reaction equations. The convergence result holds for the cases where convection or reaction is not present in convection- or reaction-dominated problems. A novel technique of analysis is developed by using the superconvergence of the scalar displacement variable instead of the quasi-orthogonality for the stress and displacement variables, and without marking the oscillation dependent on discrete solutions and data. We show that AMFEM is a contraction of the error of the stress and displacement variables plus some quantity. Numerical experiments confirm the theoretical results.

关 键 词：convection instead posteriori marking meshes projection interpolation holds interior satisfy 

分 类 号：O241.82[理学—计算数学]