# Meeting Details

Title: A posteriori error estimation, adaptive mixed FEM and convergence for convection-diffusion-reaction equations CCMA PDEs and Numerical Methods Seminar Series Xiaoping Xie, School of Mathematical Sciences Sichuan University Chengdu 610064, China A new technique of residual-type a posteriori error analysis is developed for the lowest-order Raviart-Thomas mixed finite element discretizations of convection-diffusion-reaction equations in two- or three-dimension. Both centered mixed scheme and upwind-mixed scheme are considered. The a posteriori error estimators, derived for the stress variable error plus scalar displacement error in $L^{2}$-norm, can be directly computed with the solutions of the mixed schemes without any additional cost, and are full robust with respect to inhomogeneities and anisotropy of the diffusion-dispersion tensor. Local efficiency dependent on local or global variations in coefficients is obtained without any saturation assumption, and holds from the cases where convection or reaction are not present to convection-or reaction-dominated problems. An adaptive mixed FEM is also proposed based the a posteriori error estimation. The convergence is analyzed without using any quasi orthogonality for stress and displacement variables and without marking oscillation dependent on discrete solutions and data. Numerical experiments are reported to verify the theoretical results. This is a joint work with Shaohong Du (Chongqing Jiaotong University).