An Adaptive Finite Element Method for Stationary Incompressible Thermal Flow Based on Projection Error Estimation

Abstract

An adaptive finite element method is presented for the stationary incompressible thermal flow problems. A reliable a posteriori error estimator based on a projection operator is proposed and it can be computed easily and implemented in parallel. Finally, three numerical examples are given to illustrate the efficiency of the adaptive finite element method. We also show that the adaptive strategy is effective to detect local singularities in the physical model of square cavity stationary flow in the third example.

The Crank‐Nicolson Extrapolation Stabilized Finite Element Method for Natural Convection Problem

“…Many authors have worked hard to study for a great variety of efficient numerical schemes for the natural convection problem [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] and relevant research [18,19]. We mention only a few papers here.…”