2024/12/05 by Hailong Guo, Zhimin Zhang, Guo, Hailong +1
Engineering · Materials Science · #Advanced Surface Polishing Techniques #Advanced ceramic materials synthesis #Tunneling and Rock Mechanics
paper · pdf · doi:10.48550/arxiv.2412.03787
Post-processing techniques are essential tools for enhancing the accuracy of finite element approximations and achieving superconvergence. Among these, recovery techniques stand out as vital methods, playing significant roles in both post-processing and pre-processing. This paper provides an overview of recent developments in recovery techniques and their applications in adaptive computations. The discussion encompasses both gradient recovery and Hessian recovery methods. To establish the superconvergence properties of these techniques, two theoretical frameworks are introduced. Applications of these methods are demonstrated in constructing asymptotically exact \it a posteriori error estimators for second-order elliptic equations, fourth-order elliptic equations, and interface problems. Numerical experiments are performed to evaluate the asymptotic exactness of recovery type a posteriori error estimators.