Recovery-based error estimator for the natural-convection problem based on penalized finite element method

Abstract

Purpose This paper aims to proposes and analyzes a novel recovery-based posteriori error estimator for the stationary natural-convection problem based on penalized finite element method. Design/methodology/approach The optimal error estimates of the penalty FEM are established by using the lower-order finite element pair P1-P0-P1 which does not satisfy the discrete inf-sup condition. Besides, a new recovery type posteriori estimator in view of the gradient recovery and superconvergent theory to deal with the discontinuity of the gradient of numerical solution. Findings The stability, accuracy and efficiency of the proposed method are confirmed by several numerical investigations. Originality/value The provided reliability and efficiency analysis is shown that the true error can be effectively bounded by the recovery-based error estimator.

A positivity-preserving nonlinear finite volume scheme for radionuclide transport calculations in geological radioactive waste repository

“…Potier, 2005; Lipnikov et al , 2007; Sheng and Yuan, 2012; Wu and Gao, 2014; Lipnikov et al , 2009; Peng et al , 2019; Xiao et al , 2019; Huang et al , 2019; Xiao et al , 2018; Xiao et al , 2017; Sun et al , 2019). Compared with the finite element method and finite difference method, the local conservation property of finite volume method is an important advantage (He et al , 2007; Huang and Feng, 2013; Feng et al , 2012; He and Feng, 2013; Wang et al , 2019; Li et al , 2019; Wen et al , 2016). Currently, the positivity-preserving discretization method for the diffusion term has been deeply studied.…”