A two-grid method based on Newton iteration for the Navier–Stokes equations |
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Authors: | Xiaoxia Dai Xiaoliang Cheng |
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Institution: | aDepartment of Mathematics, Zhejiang University, Hangzhou 310027, PR China |
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Abstract: | In this paper, we consider a two-grid method for resolving the nonlinearity in finite element approximations of the equilibrium Navier–Stokes equations. We prove the convergence rate of the approximation obtained by this method. The two-grid method involves solving one small, nonlinear coarse mesh system and two linear problems on the fine mesh which have the same stiffness matrix with only different right-hand side. The algorithm we study produces an approximate solution with the optimal asymptotic in h and accuracy for any Reynolds number. Numerical example is given to show the convergence of the method. |
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Keywords: | Navier– Stokes equations Two-grid Newton method |
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