A posteriori error estimation and adaptive computation of conduction convection problems

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

“…Remark 3.6 If the parameter δ K = αh 2 K = 0 in (2), Theorem 3.5 reduces to the result of Zhang et al [15] (Theorem 4.1). That is, this paper generalizes the results of Zhang et al [15] to the stabilized FEMs.…”

“…For the inequality (14), as the analysis is very closely to the procedure [15] and the method is standard, we omit the proof. The readers may find more details in [15,[25][26].…”

“…for an approximation solutionũ h = (u h , p h , T h ) (see [15]). We now continue to derive the posteriori error estimators.…”

“…The posteriori error estimators are key ingredients in the design of adaptive methods [16][17] . There are many literatures on deriving such estimators for the finite element approximation of linear and nonlinear variational problems and for standard Galerkin and mixed finite element formulations, e.g., [15,[18][19][20][21][22][23][24][25][26][27][28]. Verfürth [23,25] have developed a general theory to derive the posteriori error estimates for nonlinear equations, which has been successefully applied in [15,22,[26][27].…”

“…Luo and Lu [6] , Sun et al [7] , and Luo et al [8] applied the least squares Galerkin/Petrov FEM to conduction convection problems, and obtained optimal order error estimates. There are many works devoting to the development of efficient numerical schemes for these equations, e.g., [9][10][11][12][13][14][15].…”