| RESIDUAL A POSTERIORI ERROR ESTIMATE OF A NEW TWO-LEVEL METHOD FOR STEADY NAVIER-STOKES EQUATIONS |
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| 作者姓名： | Chunfeng REN Yichen MA |
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| 作者单位： | College of Science, Xi＇an Jiaotong University, Xi＇an 710049, China. |
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| 基金项目： | The research is supported by the National Science Foundation of China （No： 10371096）. |
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| 摘 要： | Residual-based a posteriori error estimate for conforming finite element solutions of incom-pressible Navier-Stokes equations,which is computed with a new two-level method that is differentfrom Volker John,is derived.A posteriori error estimate contains additional terms in comparison tothe estimate for the solution obtained by the standard finite element method.The importance of theadditional terms in the error estimates is investigated by studying their asymptotic behavior.For opti-mal scaled meshes,these bounds are not of higher order than the convergence of discrete solution.Thetwo-level method aims to solve the nonlinear problem on a coarse grid with less computational work,then to solve the linear problem on a fine grid,which is superior to the usual finite element methodsolving a similar nonlinear problem on the fine grid.
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| 关 键 词： | 残差 误差分析 双层法 稳定NAVIER-STOKES方程 |
| 收稿时间： | 2005-03-29 |
| 修稿时间： | 2005-03-29 |
Residual a Posteriori Error Estimate of a New Two-Level Method for Steady Navier-Stokes Equations |
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| Chunfeng REN Yichen MA.RESIDUAL A POSTERIORI ERROR ESTIMATE OF A NEW TWO-LEVEL METHOD FOR STEADY NAVIER-STOKES EQUATIONS[J].Journal of Systems Science and Complexity,2006,19(4):478-490. |
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| Authors: | Chunfeng Ren Yichen Ma |
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| Institution: | (1) College of Science, Xi’an Jiaotong University, Xi’an, 710049, China |
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| Abstract: | Residual-based a posteriori error estimate for conforming finite element solutions of incompressible Navier-Stokes equations, which is computed with a new two-level method that is different from Volker John, is derived. A posteriori error estimate contains additional terms in comparison to the estimate for the solution obtained by the standard finite element method. The importance of the additional terms in the error estimates is investigated by studying their asymptotic behavior. For optimal scaled meshes, these bounds are not of higher order than the convergence of discrete solution. The two-level method aims to solve the nonlinear problem on a coarse grid with less computational work, then to solve the linear problem on a fine grid, which is superior to the usual finite element method solving a similar nonlinear problem on the fine grid. |
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| Keywords: | Finite element method Navier-Stokes equations residual-based a posteriori error estimate two-level method |
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