• 论文 • 上一篇
唐跃龙, 华玉春
唐跃龙, 华玉春. 半线性抛物最优控制问题全离散插值系数有限元方法的收敛性分析[J]. 计算数学, 2023, 45(1): 130-140.
Tang Yuelong, Hua Yuchun. CONVERGENCE ANALYSIS OF FULLY DISCRETE INTERPOLATED COEFFICIENT FINITE ELEMENTS FOR SEMILINEAR PARABOLIC OPTIMAL CONTROL PROBLEMS[J]. Mathematica Numerica Sinica, 2023, 45(1): 130-140.
Tang Yuelong, Hua Yuchun
MR(2010)主题分类:
分享此文:
[1] Lions J. Optimal Control of Systems Governed by Partial Differential Equations[M]. Berlin:Springer-Verlag, 1971. [2] Liu W, Yan N. Adaptive Finite Element Methods for Optimal Control Governed by PDEs[M]. Beijing:Science Press, 2008. [3] Chen Y, Lu Z. High Efficient and Accuracy Numerical Methods for Optimal Control Problems[M]. Beijing:Science Press, 2015. [4] Liu W, Yan N. A posteriori error estimates for control problems governed by nonlinear elliptic equations[J]. Appl. Numer. Math., 2003, 43:173-187. [5] Chen Y, Dai Y. Superconvergence for optimal control problems governed by semi-linear elliptic equations[J]. J. Sci. Comput., 2009, 39:206-221. [6] Tang Y, Chen Y. Superconvergence analysis of fully discrete finite element methods for semilinear parabolic optimal control problems[J]. Front. Math. China, 2013, 8(2):443-464. [7] Zlamal M. Finite element methods for nonlinear parabolic equations[J]. RAIRO Model. Anal. Numer., 1997, 11:93-107. [8] Larsson S, Thomee V, Zhang N. Interpolation of coefficients and transformation of the dependent variable in finite element methods for the non-linear heat equation[J]. Math. Meth. Appl. Sci., 1989, 11(1):105-124. [9] Xiong Z, Chen Y. A rectangular finite volume element for a semilinear elliptic equation[J]. J. Sci. Comput., 2008, 36:177-179. [10] Xiong Z, Chen Y. Finite volume element method with interpolation coefficients for two-point boundary value problem of semilinear differential equation[J]. Comput. Meth. Appl. Mech. Engry., 2007, 196:3798-3804. [11] Lu Z, Cao L, Li L. Interpolation coefficients mixed finite element methods for general semilinear Dirichlet boundary elliptic optimal control problems[J]. Appl. Anal., 2018, 97(14):2496-2509. [12] 曹龙舟, 鲁祖亮, 李林. 非线性抛物最优控制问题插值系数混合有限元解的先验误差估计[J]. 云南民族大学学报:自然科学版, 2017, 26(4):299-305. [13] Liu W, Tiba T. Error estimates for the finite element approximation of a class of nonlinear optimal control problems[J]. J. Numer. Funct. Optim., 2001, 22:953-972. [14] Tang Y, Hua Y. Superconvergence of splitting positive definite mixed finite element for parabolic optimal control problems[J]. Anal. Appl., 2018, 97(16):2778-2793. [15] Chen Y, Lu Z, Huang Y. Superconvergence of triangular Raviart-Thomas mixed finite element methods for bilinear constrained optimal control problem[J]. Comput. Math. Appl., 2013, 66(8):1498-1513. [16] Li R, Liu W, Yan N. A posteriori error estimates of recovery type for distributed convex optimal control problems[J]. J. Sci. Comput., 2002, 41(5):1321-1349. |
[1] | 杨学敏, 牛晶, 姚春华. 椭圆型界面问题的破裂再生核方法[J]. 计算数学, 2022, 44(2): 217-232. |
[2] | 古振东. 非线性弱奇性Volterra积分方程的谱配置法[J]. 计算数学, 2021, 43(4): 426-443. |
[3] | 李旭, 李明翔. 连续Sylvester方程的广义正定和反Hermitian分裂迭代法及其超松弛加速[J]. 计算数学, 2021, 43(3): 354-366. |
[4] | 古振东, 孙丽英. 非线性第二类Volterra积分方程的Chebyshev谱配置法[J]. 计算数学, 2020, 42(4): 445-456. |
[5] | 王志强, 文立平, 朱珍民. 时间延迟扩散-波动分数阶微分方程有限差分方法[J]. 计算数学, 2019, 41(1): 82-90. |
[6] | 陈圣杰, 戴彧虹, 徐凤敏. 稀疏线性规划研究[J]. 计算数学, 2018, 40(4): 339-353. |
[7] | 古振东, 孙丽英. 一类弱奇性Volterra积分微分方程的级数展开数值解法[J]. 计算数学, 2017, 39(4): 351-362. |
[8] | 刘丽华, 马昌凤, 唐嘉. 求解广义鞍点问题的一个新的类SOR算法[J]. 计算数学, 2016, 38(1): 83-95. |
[9] | 黄娜, 马昌凤, 谢亚君. 求解非对称代数Riccati 方程几个新的预估-校正法[J]. 计算数学, 2013, 35(4): 401-418. |
[10] | 任志茹. 三阶线性常微分方程Sinc方程组的结构预处理方法[J]. 计算数学, 2013, 35(3): 305-322. |
[11] | 陈绍春, 梁冠男, 陈红如. Zienkiewicz元插值的非各向异性估计[J]. 计算数学, 2013, 35(3): 271-274. |
[12] | 张亚东, 石东洋. 各向异性网格下抛物方程一个新的非协调混合元收敛性分析[J]. 计算数学, 2013, 35(2): 171-180. |
[13] | 陈争, 马昌凤. 求解非线性互补问题一个新的 Jacobian 光滑化方法[J]. 计算数学, 2010, 32(4): 361-372. |
[14] | 来翔, 袁益让. 一类三维拟线性双曲型方程交替方向有限元法[J]. 计算数学, 2010, 32(1): 15-36. |
[15] | 蔚喜军. 非线性波动方程的交替显-隐差分方法[J]. 计算数学, 1998, 20(3): 225-238. |
阅读次数 | ||||||
全文 |
|
|||||
摘要 |
|
|||||