Recently, a reliable posteriori error estimate was developed, mainly based on the element residual method, for a class of steady state incompressible Navier--Stokes equations. In this paper, using this error estimate, a three-step \hp adaptive strategy is developed to solve incompressible flow problems. The goal of developing an \hp adaptive strategy is to obtain accurate approximate solutions while minimizing computational costs. The basic idea of the three-step h-p adaptive strategy is to solve for the system on the three consecutive meshes, i.e. an initial mesh, an intermediate h - adaptive mesh, and a final h-p adaptive mesh. Each new adaptive mesh is obtained by estimating the error on the previous mesh and executing a single h - or p - refinement procedure on the previous mesh according to the results of the adaptive strategy. Numerical results indicate that the proposed three-step adaptive strategy produces accurate solutions while keeping the total computational costs under control.
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