Interpolation coefficients mixed finite element methods and L<SUP>∞</SUP> -error estimates for nonlinear optimal control problem

Zuliang Lu; Shuhua Zhang; Longzhou Cao; Lin Li; Yin Yang

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Interpolation coefficients mixed finite element methods and L^∞ -error estimates for nonlinear optimal control problem

机译：非线性最优控制问题的插值系数混合有限元方法和L ^{∞-误差估计}

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In this paper, we investigate L∞ -error estimates for the convex optimal control problemgoverned by nonlinear elliptic equations using interpolation coefficients mixed finite elementmethods. By using the interpolation coefficient thought to process the nonlinear term ofequations, we present the mixed finite element approximation with interpolated coefficients fornonlinear optimal control problem. We derive L∞ -error estimates for the interpolation coefficientsmixed finite element approximation of nonlinear optimal control problem. Finally somenumerical examples are given to confirm our theoretical results.

机译：在本文中，我们使用插值系数混合有限元方法研究了非线性椭圆方程所控制的凸最优控制问题的L∞误差估计。通过使用插值系数思想来处理方程的非线性项，针对非线性最优控制问题，我们提出了带有插值系数的混合有限元逼近。我们为非线性最优控制问题的内插系数混合有限元逼近推导了L∞误差估计。最后，通过数值例子验证了我们的理论结果。

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《Journal of Mathematical Inequalities》 |2017年第4期|共17页
作者
Zuliang Lu; Shuhua Zhang; Longzhou Cao; Lin Li; Yin Yang;
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1. New a posteriori $L^{infty }(L^2) $ and $L^2(L^2)$-error estimates of mixed finite element methods for general nonlinear parabolic optimal control problems [J] . Lu Zuliang Applications of mathematics . 2016,第2期

机译：新的后验$ L ^ { infty}（L ^ 2）$和$ L ^ 2（L ^ 2）$的误差估计，适用于一般非线性抛物线最优控制问题的混合有限元方法
2. New a posteriori L (a)(L (2)) and L (2)(L (2))-error estimates of mixed finite element methods for general nonlinear parabolic optimal control problems [J] . Lu Zuliang Applications of Mathematics . 2016,第2期

机译：新的后验L（a）（L（2））和L（2）（L（2））误差-一般非线性抛物线型最优控制问题的混合有限元方法的误差估计
3. Interpolation coefficients mixed finite element methods for general semilinear Dirichlet boundary elliptic optimal control problems [J] . Lu Zuliang, Cao Longzhou, Li Lin Applicable Analysis . 2018,第13a16期

机译：插值系数混合有限元方法通用半线性脱芯边界椭圆型最佳控制问题
4. A priori error estimates of mixed finite element methods for nonlinear quadratic convex optimal control problem [C] . Zhang H. W., Lu Z. L. International Conference on Electrical Engineering, Computing Science and Automatic Control . 2008

机译：非线性二次凸出最优控制问题混合有限元方法的先验误差估计
5. Local a posteriori error estimates and adaptive control of pollution effects in the finite element method. [D] . Liao, Xiaohai. 2002

机译：局部后验误差估计和污染影响的自适应控制的有限元方法。
6. A posteriori error estimates of spectral method for nonlinear parabolic optimal control problem [O] . Lin Li, Zuliang Lu, Wei Zhang, -1

机译：非线性抛物线最优控制问题的频谱方法后验误差估计
7. Interpolation coefficients mixed finite element methods and L^∞-error estimates for nonlinear optimal control problem [O] . Zuli ng Lu, Shu ua Zhang, Longz ou Cao, 2017

机译：插值系数混合有限元方法和L ^∞误差估计对非线性最佳控制问题
8. Optimum Mixed Finite Element Nonlinear Galerkin Method for the Navier-Stokes211 Equations I: Error Estimates for Spatial Discretization [R] . He, Y., Mattheij, R. M. M. 1997

机译：Navier-stokes211方程的最优混合有限元非线性Galerkin方法I：空间离散化的误差估计

Interpolation coefficients mixed finite element methods and L∞ -error estimates for nonlinear optimal control problem

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Interpolation coefficients mixed finite element methods and L^∞ -error estimates for nonlinear optimal control problem