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 pres...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.展开更多
基金supported by Education Science Foundation of Chongqing(Grant No.KJ120420)National Natural Science Foundation of China(Grant No.11171239)+1 种基金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
文摘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.
