Three-Step H-P Adaptive Strategy for the Incompressible Navier-Stokes Equations

Abstract

Recently, a reliable a 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 h-p adaptive strategy is developed to solve incompressible flow problems. The goal of developing an h-p 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.