Adaptive mixed least squares Galerkin/Petrov finite element method for stationary conduction convection problems

Abstract

An adaptive mixed least squares Galerkin/Petrov finite element method (FEM) is developed for stationary conduction convection problems. The mixed least squares Galerkin/Petrov FEM is consistent and stable for any combination of discrete velocity and pressure spaces without requiring the Babuska-Brezzi stability condition. Using the general theory of Verfürth, the posteriori error estimates of the residual type are derived. Finally, numerical tests are presented to illustrate the effectiveness of the method.

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

“…To show the effectiveness of our adaptive method and the adaptive procedures based on the residual posteriori error estimator [21,30,31], in which the detailed formulation of the local error estimator is presented.…”