| Stokes方程的压力梯度局部投影间断有限元法 |
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| 引用本文： | 骆艳,冯民富.Stokes方程的压力梯度局部投影间断有限元法[J].计算数学,2008,30(1):25-36. |
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| 作者姓名： | 骆艳 冯民富 |
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| 作者单位： | 1. 电子科技大学应用数学学院,成都,610054
2. 电子科技大学应用数学学院,成都,610054;四川大学数学学院,成都,610064 |
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| 基金项目： | 四川省科技攻关课题(编号：05GG006-006-2)资助项目 |
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| 摘 要： | 本文对定常的Stokes方程提出了一种新的间断有限元法,通过将通常的间断Galerkin有限元法与压力梯度局部投影相结合,建立了一个稳定的间断有限元格式,对速度和压力的任意分片多项式空间P_l(K),P_m(K)的间断有限元逼近证明了解的存在唯一性,给出了关于速度和压力的L~2范数的最优误差估计.
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| 关 键 词： | 间断Galerkin有限元法 压力梯度投影 Stokes问题 误差估计 |
| 收稿时间： | 2006-06-22 |
| 修稿时间： | 2006年6月22日 |
A DISCONTINUOUS ELEMENT PRESSURE GRADIENT STABILIZATIONS FOR THE STOKES EQUATIONS BASED ON LOCAL PROJECTIONS |
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| Luo Yan,Feng Minfu.A DISCONTINUOUS ELEMENT PRESSURE GRADIENT STABILIZATIONS FOR THE STOKES EQUATIONS BASED ON LOCAL PROJECTIONS[J].Mathematica Numerica Sinica,2008,30(1):25-36. |
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| Authors: | Luo Yan Feng Minfu |
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| Institution: | Luo Yan (School of Applied Mathematics,University of Electronic Science and Technology of China,Chengdu 610054,China) Feng Minfu (School of Applied Mathematics,University of Electronic Science and Technology of China,Chengdu 610054,China;Department of Mathematics,Sichuan University,Chengdu 610064,China) |
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| Abstract: | In this paper,we derive a pressure gradient discontinuous finite element formulation for Stokes equations based on local projections.This new formulation is stable and consistent for any combination of discrete discontinuous velocity and pressure spaces,when polynomials of degree l are used for each component of velocity and polynomials of m for the pressure, for any l(?)1 and m(?)0.Optimal error estimates for the approximation of both velocity and pressure in L~2 norm are obtained for the Stokes problems. |
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| Keywords: | discontinuous finite element methods pressure gradient projection methods Stokes equations error estimation |
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