Deferred defect‐correction finite element method for the Darcy‐Brinkman model

Abstract

This paper proposes a deferred defect-correction method for the time-dependent nonlinear Darcy-Brinkman model based on the mixed finite element method. The presented method combines the deferred correction strategy with the defect-correction method and involves two steps. In the first step, a defect Darcy-Brinkman model is solved. Then in the second step, a correction Darcy-Brinkman model based on the deferred correction approach is solved. Moreover, unconditional stability and convergence of the presented method are deduced. Finally, several numerical examples are given to support the theoretical analysis.