Chen, Yanping; Chen, Zhenrong; Huang, Yunqing Generalized Jacobi spectral Galerkin method for fractional-order Volterra integro-differential equations with weakly singular kernels. (English) Zbl 07806676 J. Comput. Math. 42, No. 2, 355-371 (2024). MSC: 65L05 65L20 65L50 PDFBibTeX XMLCite \textit{Y. Chen} et al., J. Comput. Math. 42, No. 2, 355--371 (2024; Zbl 07806676) Full Text: DOI
Lin, Xiuxiu; Chen, Yanping; Huang, Yunqing Error estimates of hp spectral element methods in nonlinear optimal control problem. (English) Zbl 07787313 J. Nonlinear Sci. 34, No. 1, Paper No. 21, 23 p. (2024). MSC: 49J20 65K10 65N35 PDFBibTeX XMLCite \textit{X. Lin} et al., J. Nonlinear Sci. 34, No. 1, Paper No. 21, 23 p. (2024; Zbl 07787313) Full Text: DOI
Yang, Zhengya; Chen, Xuejuan; Chen, Yanping; Wang, Jing Accurate numerical simulations for fractional diffusion equations using spectral deferred correction methods. (English) Zbl 07784331 Comput. Math. Appl. 153, 123-129 (2024). MSC: 65-XX 35R11 65M70 26A33 65M12 65M06 PDFBibTeX XMLCite \textit{Z. Yang} et al., Comput. Math. Appl. 153, 123--129 (2024; Zbl 07784331) Full Text: DOI
Zheng, Weishan; Chen, Yanping; Zhou, Jianwei A Legendre spectral method for multidimensional partial Volterra integro-differential equations. (English) Zbl 07738623 J. Comput. Appl. Math. 436, Article ID 115302, 17 p. (2024). MSC: 65-XX 35R09 65M12 65M70 PDFBibTeX XMLCite \textit{W. Zheng} et al., J. Comput. Appl. Math. 436, Article ID 115302, 17 p. (2024; Zbl 07738623) Full Text: DOI
Tian, Zhikun; Chen, Yanping; Huang, Yunqing; Wang, Jianyun Two-grid mixed finite element method for two-dimensional time-dependent Schrödinger equation. (English) Zbl 1528.65083 Math. Methods Appl. Sci. 46, No. 12, 12759-12776 (2023). MSC: 65M60 65M12 35Q55 PDFBibTeX XMLCite \textit{Z. Tian} et al., Math. Methods Appl. Sci. 46, No. 12, 12759--12776 (2023; Zbl 1528.65083) Full Text: DOI
Lin, Xiuxiu; Chen, Yanping; Huang, Yunqing Spectral approximation for optimal control problems governed by first bi-harmonic equation. (English) Zbl 07777335 Numer. Methods Partial Differ. Equations 39, No. 4, 2808-2822 (2023). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{X. Lin} et al., Numer. Methods Partial Differ. Equations 39, No. 4, 2808--2822 (2023; Zbl 07777335) Full Text: DOI
Zheng, Weishan; Chen, Yanping A spectral collocation method for a nonlinear multidimensional Volterra integral equation. (English) Zbl 07776982 Numer. Methods Partial Differ. Equations 39, No. 2, 1767-1777 (2023). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{W. Zheng} and \textit{Y. Chen}, Numer. Methods Partial Differ. Equations 39, No. 2, 1767--1777 (2023; Zbl 07776982) Full Text: DOI
Tang, Bo; Chen, Yan-ping; Xie, Bin; Lin, Xiu-xiu A novel error analysis of spectral method for the anomalous subdiffusion problems with multi-term time-fractional derivative. (English) Zbl 07767311 Acta Math. Appl. Sin., Engl. Ser. 39, No. 4, 943-961 (2023). MSC: 41A60 PDFBibTeX XMLCite \textit{B. Tang} et al., Acta Math. Appl. Sin., Engl. Ser. 39, No. 4, 943--961 (2023; Zbl 07767311) Full Text: DOI
Chen, Yanping; Lin, Xiuxiu; Zhang, Mengjuan; Huang, Yunqing Stability and convergence of \(L1\)-Galerkin spectral methods for the nonlinear time fractional cable equation. (English) Zbl 07707436 East Asian J. Appl. Math. 13, No. 1, 22-46 (2023). MSC: 65-XX 35R11 65M12 65M70 PDFBibTeX XMLCite \textit{Y. Chen} et al., East Asian J. Appl. Math. 13, No. 1, 22--46 (2023; Zbl 07707436) Full Text: DOI
Tian, Zhikun; Chen, Yanping; Wang, Jianyun A two-grid discretization method for nonlinear Schrödinger equation by mixed finite element methods. (English) Zbl 1524.65602 Comput. Math. Appl. 130, 10-20 (2023). MSC: 65M60 65M06 65N30 65M12 35Q55 65M15 65M55 35Q41 65N50 PDFBibTeX XMLCite \textit{Z. Tian} et al., Comput. Math. Appl. 130, 10--20 (2023; Zbl 1524.65602) Full Text: DOI
Lin, Xiuxiu; Chen, Yanping; Huang, Yunqing A priori and a posteriori error analysis of hp spectral element discretization for optimal control problems with elliptic equations. (English) Zbl 1505.49007 J. Comput. Appl. Math. 423, Article ID 114960, 15 p. (2023). MSC: 49J20 65K10 65N35 PDFBibTeX XMLCite \textit{X. Lin} et al., J. Comput. Appl. Math. 423, Article ID 114960, 15 p. (2023; Zbl 1505.49007) Full Text: DOI
Zheng, Weishan; Chen, Yanping Numerical approach for weakly singular equation with nonlinear delay. (English) Zbl 1507.65302 Bull. Malays. Math. Sci. Soc. (2) 45, No. 6, 2821-2842 (2022). MSC: 65R20 45E05 PDFBibTeX XMLCite \textit{W. Zheng} and \textit{Y. Chen}, Bull. Malays. Math. Sci. Soc. (2) 45, No. 6, 2821--2842 (2022; Zbl 1507.65302) Full Text: DOI
Chen, Zhenrong; Chen, Yanping; Huang, Yunqing Piecewise spectral collocation method for second order Volterra integro-differential equations with nonvanishing delay. (English) Zbl 1513.65403 Adv. Appl. Math. Mech. 14, No. 6, 1333-1356 (2022). MSC: 65M70 65M12 65M15 65D32 35R09 45D05 45K05 45J05 65R20 PDFBibTeX XMLCite \textit{Z. Chen} et al., Adv. Appl. Math. Mech. 14, No. 6, 1333--1356 (2022; Zbl 1513.65403) Full Text: DOI
Chen, Yanping; Wang, Lina; Yi, Lijun Exponential convergence of \(hp\)-discontinuous Galerkin method for nonlinear Caputo fractional differential equations. (English) Zbl 1492.65356 J. Sci. Comput. 92, No. 3, Paper No. 99, 27 p. (2022). MSC: 65R20 65L60 65L05 65L70 PDFBibTeX XMLCite \textit{Y. Chen} et al., J. Sci. Comput. 92, No. 3, Paper No. 99, 27 p. (2022; Zbl 1492.65356) Full Text: DOI
Yang, Yin; Wang, Jindi; Chen, Yanping; Liao, Hong-lin Compatible \(L^2\) norm convergence of variable-step L1 scheme for the time-fractional MBE model with slope selection. (English) Zbl 07568562 J. Comput. Phys. 467, Article ID 111467, 16 p. (2022). MSC: 65Mxx 35Rxx 35Qxx PDFBibTeX XMLCite \textit{Y. Yang} et al., J. Comput. Phys. 467, Article ID 111467, 16 p. (2022; Zbl 07568562) Full Text: DOI arXiv
Zheng, Weishan; Chen, Yanping A spectral method for a weakly singular Volterra integro-differential equation with pantograph delay. (English) Zbl 1513.65541 Acta Math. Sci., Ser. B, Engl. Ed. 42, No. 1, 387-402 (2022). MSC: 65R20 45J05 45D05 PDFBibTeX XMLCite \textit{W. Zheng} and \textit{Y. Chen}, Acta Math. Sci., Ser. B, Engl. Ed. 42, No. 1, 387--402 (2022; Zbl 1513.65541) Full Text: DOI
Chen, Yanping; Lin, Xiuxiu; Huang, Yunqing Error analysis of spectral approximation for space-time fractional optimal control problems with control and state constraints. (English) Zbl 1524.49053 J. Comput. Appl. Math. 413, Article ID 114293, 15 p. (2022). MSC: 49M25 35R11 49J20 26A33 65M15 PDFBibTeX XMLCite \textit{Y. Chen} et al., J. Comput. Appl. Math. 413, Article ID 114293, 15 p. (2022; Zbl 1524.49053) Full Text: DOI
Liu, Libin; Chen, Yanping; Liang, Ying Numerical analysis of a nonlinear singularly perturbed delay Volterra integro-differential equation on an adaptive grid. (English) Zbl 1499.65282 J. Comput. Math. 40, No. 2, 258-274 (2022). MSC: 65L05 65L20 65L50 PDFBibTeX XMLCite \textit{L. Liu} et al., J. Comput. Math. 40, No. 2, 258--274 (2022; Zbl 1499.65282) Full Text: DOI
Mao, Wenting; Chen, Yanping; Wang, Huasheng A posteriori error estimations of the Petrov-Galerkin methods for fractional Helmholtz equations. (English) Zbl 07490867 Numer. Algorithms 89, No. 3, 1095-1127 (2022). MSC: 65-XX 35-XX PDFBibTeX XMLCite \textit{W. Mao} et al., Numer. Algorithms 89, No. 3, 1095--1127 (2022; Zbl 07490867) Full Text: DOI
Zhang, Jinling; Chen, Yanping; Huang, Yunqing; Huang, Fenglin A posteriori error estimates for \(hp\) spectral element approximation of elliptic control problems with integral control and state constraints. (English) Zbl 1499.65693 Adv. Appl. Math. Mech. 14, No. 2, 469-493 (2022). MSC: 65N30 35Q93 49K20 49M25 65K10 PDFBibTeX XMLCite \textit{J. Zhang} et al., Adv. Appl. Math. Mech. 14, No. 2, 469--493 (2022; Zbl 1499.65693) Full Text: DOI
Wang, Huasheng; Chen, Yanping; Huang, Yunqing; Mao, Wenting A Petrov-Galerkin spectral method for fractional convection-diffusion equations with two-sided fractional derivative. (English) Zbl 1480.65356 Int. J. Comput. Math. 98, No. 3, 536-551 (2021). MSC: 65N35 65N12 65N15 PDFBibTeX XMLCite \textit{H. Wang} et al., Int. J. Comput. Math. 98, No. 3, 536--551 (2021; Zbl 1480.65356) Full Text: DOI
Tang, Bo; Chen, Yanping; Lin, Xiuxiu A posteriori error estimates of spectral Galerkin methods for multi-term time fractional diffusion equations. (English) Zbl 1524.35719 Appl. Math. Lett. 120, Article ID 107259, 8 p. (2021). MSC: 35R11 65M12 65M06 65R20 65M70 PDFBibTeX XMLCite \textit{B. Tang} et al., Appl. Math. Lett. 120, Article ID 107259, 8 p. (2021; Zbl 1524.35719) Full Text: DOI
Leng, Haitao; Chen, Yanping Residual-type a posteriori error analysis of HDG methods for Neumann boundary control problems. (English) Zbl 1465.65053 Adv. Comput. Math. 47, No. 3, Paper No. 30, 20 p. (2021). MSC: 65K10 65N30 49M25 49M41 PDFBibTeX XMLCite \textit{H. Leng} and \textit{Y. Chen}, Adv. Comput. Math. 47, No. 3, Paper No. 30, 20 p. (2021; Zbl 1465.65053) Full Text: DOI arXiv
Shi, Xiulian; Chen, Yanping; Huang, Yunqing; Huang, Fenglin Spectral collocation methods for second-order Volterra integro-differential equations with weakly singular kernels. (English) Zbl 1488.65759 Adv. Appl. Math. Mech. 12, No. 2, 480-502 (2020). MSC: 65R20 65M70 45D05 45J05 PDFBibTeX XMLCite \textit{X. Shi} et al., Adv. Appl. Math. Mech. 12, No. 2, 480--502 (2020; Zbl 1488.65759) Full Text: DOI
Wang, Huasheng; Chen, Yanping; Huang, Yunqing; Mao, Wenting A posteriori error estimates of the Galerkin spectral methods for space-time fractional diffusion equations. (English) Zbl 1488.65521 Adv. Appl. Math. Mech. 12, No. 1, 87-100 (2020). MSC: 65M70 65M12 65N35 65M60 65N30 65M15 26A33 35R11 PDFBibTeX XMLCite \textit{H. Wang} et al., Adv. Appl. Math. Mech. 12, No. 1, 87--100 (2020; Zbl 1488.65521) Full Text: DOI
Lin, Xiuxiu; Chen, Yanping; Huang, Yunqing Galerkin spectral approximation of optimal control problems with \(L^2\)-norm control constraint. (English) Zbl 1448.49028 Appl. Numer. Math. 150, 418-432 (2020). MSC: 49K20 65N35 65N15 35J99 PDFBibTeX XMLCite \textit{X. Lin} et al., Appl. Numer. Math. 150, 418--432 (2020; Zbl 1448.49028) Full Text: DOI
Lin, Xiuxiu; Chen, Yanping; Huang, Yunqing A posteriori error estimates of \(hp\) spectral element methods for optimal control problems with \(L^2\)-norm state constraint. (English) Zbl 07171736 Numer. Algorithms 83, No. 3, 1145-1169 (2020). MSC: 65-XX PDFBibTeX XMLCite \textit{X. Lin} et al., Numer. Algorithms 83, No. 3, 1145--1169 (2020; Zbl 07171736) Full Text: DOI
Chen, Yanping; Lin, Xiuxiu; Huang, Yunqing; Lin, Qian \(hp\) spectral element approximation for integral state constrained optimal control problems governed by harmonic equations. (English) Zbl 1440.65244 J. Comput. Appl. Math. 371, Article ID 112716, 13 p. (2020). MSC: 65N35 65N15 65N50 31A30 49K20 93C20 35Q93 35B45 PDFBibTeX XMLCite \textit{Y. Chen} et al., J. Comput. Appl. Math. 371, Article ID 112716, 13 p. (2020; Zbl 1440.65244) Full Text: DOI
Zheng, Weishan; Chen, Yanping Numerical analysis for Volterra integral equation with two kinds of delay. (English) Zbl 1499.65779 Acta Math. Sci., Ser. B, Engl. Ed. 39, No. 2, 607-617 (2019). MSC: 65R20 45E05 PDFBibTeX XMLCite \textit{W. Zheng} and \textit{Y. Chen}, Acta Math. Sci., Ser. B, Engl. Ed. 39, No. 2, 607--617 (2019; Zbl 1499.65779) Full Text: DOI
Cai, Haotao; Chen, Yanping; Huang, Yunqing A Legendre-Petrov-Galerkin method for solving Volterra integro-differential equations with proportional delays. (English) Zbl 1499.65743 Int. J. Comput. Math. 96, No. 5, 920-934 (2019). MSC: 65R20 45E05 PDFBibTeX XMLCite \textit{H. Cai} et al., Int. J. Comput. Math. 96, No. 5, 920--934 (2019; Zbl 1499.65743) Full Text: DOI
Zheng, Weishan; Chen, Yanping; Huang, Yunqing Convergence analysis of Legendre-collocation spectral methods for second order Volterra integro-differential equation with delay. (English) Zbl 1488.65768 Adv. Appl. Math. Mech. 11, No. 2, 486-500 (2019). MSC: 65R20 45J05 45D05 PDFBibTeX XMLCite \textit{W. Zheng} et al., Adv. Appl. Math. Mech. 11, No. 2, 486--500 (2019; Zbl 1488.65768) Full Text: DOI
Leng, Haitao; Chen, Yanping; Huang, Yunqing Equivalent a posteriori error estimates for elliptic optimal control problems with \(L^1\)-control cost. (English) Zbl 1442.49036 Comput. Math. Appl. 77, No. 2, 342-356 (2019). MSC: 49M25 65N15 65N30 65N50 PDFBibTeX XMLCite \textit{H. Leng} et al., Comput. Math. Appl. 77, No. 2, 342--356 (2019; Zbl 1442.49036) Full Text: DOI
Wei, Yunxia; Chen, Yanping; Huang, Yunqing Legendre collocation method for Volterra integro-differential algebraic equation. (English) Zbl 1431.65247 Comput. Methods Appl. Math. 19, No. 4, 833-847 (2019). MSC: 65R20 45J05 PDFBibTeX XMLCite \textit{Y. Wei} et al., Comput. Methods Appl. Math. 19, No. 4, 833--847 (2019; Zbl 1431.65247) Full Text: DOI
Wei, Yunxia; Chen, Yanping A Jacobi spectral method for solving multidimensional linear Volterra integral equation of the second kind. (English) Zbl 1416.65558 J. Sci. Comput. 79, No. 3, 1801-1813 (2019). MSC: 65R20 45D05 45J05 65N12 PDFBibTeX XMLCite \textit{Y. Wei} and \textit{Y. Chen}, J. Sci. Comput. 79, No. 3, 1801--1813 (2019; Zbl 1416.65558) Full Text: DOI
Wei, Yunxia; Chen, Yanping; Shi, Xiulian; Zhang, Yuanyuan Spectral method for multidimensional Volterra integral equation with regular kernel. (English) Zbl 1416.65559 Front. Math. China 14, No. 2, 435-448 (2019). MSC: 65R20 45D05 65N12 PDFBibTeX XMLCite \textit{Y. Wei} et al., Front. Math. China 14, No. 2, 435--448 (2019; Zbl 1416.65559) Full Text: DOI
Chen, Yanping; Zhang, Jinling; Huang, Yunqing; Xu, Yeqing A posteriori error estimates of hp spectral element methods for integral state constrained elliptic optimal control problems. (English) Zbl 1421.35188 Appl. Numer. Math. 144, 42-58 (2019). MSC: 35J99 49J20 PDFBibTeX XMLCite \textit{Y. Chen} et al., Appl. Numer. Math. 144, 42--58 (2019; Zbl 1421.35188) Full Text: DOI
Yang, Yin; Chen, Yanping Spectral collocation methods for nonlinear Volterra integro-differential equations with weakly singular kernels. (English) Zbl 1406.65141 Bull. Malays. Math. Sci. Soc. (2) 42, No. 1, 297-314 (2019). MSC: 65R20 45J05 45D05 PDFBibTeX XMLCite \textit{Y. Yang} and \textit{Y. Chen}, Bull. Malays. Math. Sci. Soc. (2) 42, No. 1, 297--314 (2019; Zbl 1406.65141) Full Text: DOI
Chen, Yanping; Leng, Haitao; Yang, Wendi Error estimates of pseudostress-velocity MFEM for optimal control problems governed by Stokes equations. (English) Zbl 1403.65130 Appl. Numer. Math. 135, 407-422 (2019). MSC: 65N30 65N15 65K10 74S05 76M10 PDFBibTeX XMLCite \textit{Y. Chen} et al., Appl. Numer. Math. 135, 407--422 (2019; Zbl 1403.65130) Full Text: DOI
Yang, Xingfa; Yang, Yin; Chen, Yanping; Liu, Jie Jacobi spectral collocation method based on Lagrange interpolation polynomials for solving nonlinear fractional integro-differential equations. (English) Zbl 1488.65763 Adv. Appl. Math. Mech. 10, No. 6, 1440-1458 (2018). MSC: 65R20 45J05 45D05 35R11 PDFBibTeX XMLCite \textit{X. Yang} et al., Adv. Appl. Math. Mech. 10, No. 6, 1440--1458 (2018; Zbl 1488.65763) Full Text: DOI
Leng, Haitao; Chen, Yanping Convergence and quasi-optimality of an adaptive finite element method for optimal control problems with integral control constraint. (English) Zbl 1391.80007 Adv. Comput. Math. 44, No. 2, 367-394 (2018). MSC: 80M10 49J20 PDFBibTeX XMLCite \textit{H. Leng} and \textit{Y. Chen}, Adv. Comput. Math. 44, No. 2, 367--394 (2018; Zbl 1391.80007) Full Text: DOI
Cai, Haotao; Chen, Yanping A fractional order collocation method for second kind Volterra integral equations with weakly singular kernels. (English) Zbl 1391.45002 J. Sci. Comput. 75, No. 2, 970-992 (2018). MSC: 45D05 65R20 PDFBibTeX XMLCite \textit{H. Cai} and \textit{Y. Chen}, J. Sci. Comput. 75, No. 2, 970--992 (2018; Zbl 1391.45002) Full Text: DOI
Wei, Yunxia; Chen, Yanping; Shi, Xiulian A spectral collocation method for multidimensional nonlinear weakly singular Volterra integral equation. (English) Zbl 1377.65175 J. Comput. Appl. Math. 331, 52-63 (2018). MSC: 65R20 45D05 45J05 PDFBibTeX XMLCite \textit{Y. Wei} et al., J. Comput. Appl. Math. 331, 52--63 (2018; Zbl 1377.65175) Full Text: DOI
Liu, Xiong; Chen, Yanping Convergence analysis for the Chebyshev collocation methods to Volterra integral equations with a weakly singular kernel. (English) Zbl 1488.65750 Adv. Appl. Math. Mech. 9, No. 6, 1506-1524 (2017). MSC: 65R20 45F99 41A50 65D32 PDFBibTeX XMLCite \textit{X. Liu} and \textit{Y. Chen}, Adv. Appl. Math. Mech. 9, No. 6, 1506--1524 (2017; Zbl 1488.65750) Full Text: DOI
Liu, Shang; Chen, Yanping A new two-grid method for expanded mixed finite element solution of nonlinear reaction diffusion equations. (English) Zbl 1488.65438 Adv. Appl. Math. Mech. 9, No. 3, 757-774 (2017). MSC: 65M60 65M12 65M22 65M15 65N55 PDFBibTeX XMLCite \textit{S. Liu} and \textit{Y. Chen}, Adv. Appl. Math. Mech. 9, No. 3, 757--774 (2017; Zbl 1488.65438) Full Text: DOI
Yang, Yin; Chen, Yanping; Huang, Yunqing; Wei, Huayi Spectral collocation method for the time-fractional diffusion-wave equation and convergence analysis. (English) Zbl 1412.65168 Comput. Math. Appl. 73, No. 6, 1218-1232 (2017). MSC: 65M70 65M12 35R11 65D05 PDFBibTeX XMLCite \textit{Y. Yang} et al., Comput. Math. Appl. 73, No. 6, 1218--1232 (2017; Zbl 1412.65168) Full Text: DOI
Leng, Haitao; Chen, Yanping Convergence and quasi-optimality of an adaptive finite element method for optimal control problems on \(L^{2}\) errors. (English) Zbl 1396.65101 J. Sci. Comput. 73, No. 1, 438-458 (2017). Reviewer: Wei Gong (Beijing) MSC: 65K10 49J20 65N12 65N15 65N30 PDFBibTeX XMLCite \textit{H. Leng} and \textit{Y. Chen}, J. Sci. Comput. 73, No. 1, 438--458 (2017; Zbl 1396.65101) Full Text: DOI
Liu, Li-Bin; Chen, Yanping A-posteriori error estimation in maximum norm for a strongly coupled system of two singularly perturbed convection-diffusion problems. (English) Zbl 1353.65087 J. Comput. Appl. Math. 313, 152-167 (2017). MSC: 65L70 65L11 34B15 34E15 65L12 65L50 65L10 PDFBibTeX XMLCite \textit{L.-B. Liu} and \textit{Y. Chen}, J. Comput. Appl. Math. 313, 152--167 (2017; Zbl 1353.65087) Full Text: DOI
Shi, Xiulian; Chen, Yanping Spectral-collocation method for Volterra delay integro-differential equations with weakly singular kernels. (English) Zbl 1488.65758 Adv. Appl. Math. Mech. 8, No. 4, 648-669 (2016). MSC: 65R20 65M70 45D05 45J05 PDFBibTeX XMLCite \textit{X. Shi} and \textit{Y. Chen}, Adv. Appl. Math. Mech. 8, No. 4, 648--669 (2016; Zbl 1488.65758) Full Text: DOI
Huang, Fenglin; Chen, Yanping; Shi, Xiulian Equivalent a posteriori error estimator of spectral approximation for control problems with integral control-state constraints in one dimension. (English) Zbl 1488.49010 Adv. Appl. Math. Mech. 8, No. 3, 464-484 (2016). MSC: 49J20 65K15 65M12 65M70 PDFBibTeX XMLCite \textit{F. Huang} et al., Adv. Appl. Math. Mech. 8, No. 3, 464--484 (2016; Zbl 1488.49010) Full Text: DOI
Chen, Yanping; Huang, Fenglin Galerkin spectral approximation of elliptic optimal control problems with \(H^1\)-norm state constraint. (English) Zbl 1342.65148 J. Sci. Comput. 67, No. 1, 65-83 (2016). Reviewer: Bülent Karasözen (Ankara) MSC: 65K10 49J20 49M25 PDFBibTeX XMLCite \textit{Y. Chen} and \textit{F. Huang}, J. Sci. Comput. 67, No. 1, 65--83 (2016; Zbl 1342.65148) Full Text: DOI
Chen, Yanping; Leng, Haitao; Liu, Li-Bin Error analysis for a non-monotone FEM for a singularly perturbed problem with two small parameters. (English) Zbl 1488.65199 Adv. Appl. Math. Mech. 7, No. 2, 196-206 (2015). MSC: 65L60 65L11 65L10 PDFBibTeX XMLCite \textit{Y. Chen} et al., Adv. Appl. Math. Mech. 7, No. 2, 196--206 (2015; Zbl 1488.65199) Full Text: DOI
Yang, Yin; Chen, Yanping; Huang, Yunqing; Yang, Wei Convergence analysis of Legendre-collocation methods for nonlinear Volterra type integro equations. (English) Zbl 1488.65764 Adv. Appl. Math. Mech. 7, No. 1, 74-88 (2015). MSC: 65R20 45J05 45D05 PDFBibTeX XMLCite \textit{Y. Yang} et al., Adv. Appl. Math. Mech. 7, No. 1, 74--88 (2015; Zbl 1488.65764) Full Text: DOI
Chen, Yanping; Huang, Yunqing; Liu, Wenbin; Yan, Ningning A mixed multiscale finite element method for convex optimal control problems with oscillating coefficients. (English) Zbl 1443.49035 Comput. Math. Appl. 70, No. 4, 297-313 (2015). MSC: 49M25 65N30 PDFBibTeX XMLCite \textit{Y. Chen} et al., Comput. Math. Appl. 70, No. 4, 297--313 (2015; Zbl 1443.49035) Full Text: DOI
Hou, Chunjuan; Chen, Yanping; Lu, Zuliang A posteriori error estimates of mixed finite element solutions for fourth order parabolic control problems. (English) Zbl 1336.65111 J. Inequal. Appl. 2015, Paper No. 240, 20 p. (2015). MSC: 65K10 49J20 49M25 PDFBibTeX XMLCite \textit{C. Hou} et al., J. Inequal. Appl. 2015, Paper No. 240, 20 p. (2015; Zbl 1336.65111) Full Text: DOI
Hou, Tianliang; Chen, Yanping Superconvergence of fully discrete rectangular mixed finite element methods of parabolic control problems. (English) Zbl 1327.49049 J. Comput. Appl. Math. 286, 79-92 (2015). MSC: 49M25 49J20 49N10 49M15 65M60 65M25 PDFBibTeX XMLCite \textit{T. Hou} and \textit{Y. Chen}, J. Comput. Appl. Math. 286, 79--92 (2015; Zbl 1327.49049) Full Text: DOI
Chen, Yanping; Lin, Zhuoqing A posteriori error estimates of semidiscrete mixed finite element methods for parabolic optimal control problems. (English) Zbl 1315.49013 East Asian J. Appl. Math. 5, No. 1, 85-108 (2015). MSC: 49M25 49J20 65N30 PDFBibTeX XMLCite \textit{Y. Chen} and \textit{Z. Lin}, East Asian J. Appl. Math. 5, No. 1, 85--108 (2015; Zbl 1315.49013) Full Text: DOI
Gu, Zhendong; Chen, Yanping Piecewise Legendre spectral-collocation method for Volterra integro-differential equations. (English) Zbl 1310.65133 LMS J. Comput. Math. 18, 231-249 (2015). MSC: 65M70 45D05 45J05 PDFBibTeX XMLCite \textit{Z. Gu} and \textit{Y. Chen}, LMS J. Comput. Math. 18, 231--249 (2015; Zbl 1310.65133) Full Text: DOI
Huang, Fenglin; Chen, Yanping Error estimates for spectral approximation of elliptic control problems with integral state and control constraints. (English) Zbl 1362.49014 Comput. Math. Appl. 68, No. 8, 789-803 (2014). MSC: 49K20 35J15 65N15 65N35 65N30 49M30 PDFBibTeX XMLCite \textit{F. Huang} and \textit{Y. Chen}, Comput. Math. Appl. 68, No. 8, 789--803 (2014; Zbl 1362.49014) Full Text: DOI
Chen, Yanping; Sun, Chunmei Error estimates and superconvergence of mixed finite element methods for fourth order hyperbolic control problems. (English) Zbl 1336.65163 Appl. Math. Comput. 244, 642-653 (2014). MSC: 65M60 65M15 49M25 PDFBibTeX XMLCite \textit{Y. Chen} and \textit{C. Sun}, Appl. Math. Comput. 244, 642--653 (2014; Zbl 1336.65163) Full Text: DOI
Chen, Yanping; Lin, Yijie A posteriori error estimates for control problems governed by nonlinear elliptic equations in \(hp\)-FEM. (English) Zbl 1337.65150 Appl. Math. Comput. 238, 163-176 (2014). MSC: 65N30 65N15 49M25 PDFBibTeX XMLCite \textit{Y. Chen} and \textit{Y. Lin}, Appl. Math. Comput. 238, 163--176 (2014; Zbl 1337.65150) Full Text: DOI
Gu, Zhendong; Chen, Yanping Legendre spectral-collocation method for Volterra integral equations with non-vanishing delay. (English) Zbl 1455.65234 Calcolo 51, No. 1, 151-174 (2014). MSC: 65R20 45D05 65M70 PDFBibTeX XMLCite \textit{Z. Gu} and \textit{Y. Chen}, Calcolo 51, No. 1, 151--174 (2014; Zbl 1455.65234) Full Text: DOI
Liu, Li-Bin; Chen, Yanping A robust adaptive grid method for a system of two singularly perturbed convection-diffusion equations with weak coupling. (English) Zbl 1306.65236 J. Sci. Comput. 61, No. 1, 1-16 (2014). Reviewer: Srinivasan Natesan (Assam) MSC: 65L10 65L12 65L50 65L11 34B15 34E15 65L70 PDFBibTeX XMLCite \textit{L.-B. Liu} and \textit{Y. Chen}, J. Sci. Comput. 61, No. 1, 1--16 (2014; Zbl 1306.65236) Full Text: DOI
Wei, Yunxia; Chen, Yanping Legendre spectral collocation method for neutral and high-order Volterra integro-differential equation. (English) Zbl 1291.65390 Appl. Numer. Math. 81, 15-29 (2014). MSC: 65R20 45D05 45J05 PDFBibTeX XMLCite \textit{Y. Wei} and \textit{Y. Chen}, Appl. Numer. Math. 81, 15--29 (2014; Zbl 1291.65390) Full Text: DOI
Luo, Xianbing; Chen, Yanping; Huang, Yunqing; Hou, Tianliang Some error estimates of finite volume element method for parabolic optimal control problems. (English) Zbl 1290.49057 Optim. Control Appl. Methods 35, No. 2, 145-165 (2014). MSC: 49M25 65M08 49J20 35K20 PDFBibTeX XMLCite \textit{X. Luo} et al., Optim. Control Appl. Methods 35, No. 2, 145--165 (2014; Zbl 1290.49057) Full Text: DOI
Lu, Zuliang; Chen, Yanping A priori error estimates of mixed finite element methods for general semilinear elliptic optimal control problems. (English) Zbl 1329.65132 Comput. Math. Model. 24, No. 1, 114-135 (2013). MSC: 65K10 49J20 49M25 PDFBibTeX XMLCite \textit{Z. Lu} and \textit{Y. Chen}, Comput. Math. Model. 24, No. 1, 114--135 (2013; Zbl 1329.65132) Full Text: DOI
Chen, Yanping; Hou, Tianliang; Yi, Nianyu Variational discretization for optimal control problems governed by parabolic equations. (English) Zbl 1297.49048 J. Syst. Sci. Complex. 26, No. 6, 902-924 (2013). MSC: 49M25 49J20 35K20 65M60 PDFBibTeX XMLCite \textit{Y. Chen} et al., J. Syst. Sci. Complex. 26, No. 6, 902--924 (2013; Zbl 1297.49048) Full Text: DOI
Chen, Yanping; Lu, Zuliang; Fu, Min A posteriori error estimates for mixed finite element approximation of nonlinear quadratic optimal control problems. (English) Zbl 1264.49031 Optim. Methods Softw. 28, No. 1, 37-53 (2013). MSC: 49M25 49J20 65N30 PDFBibTeX XMLCite \textit{Y. Chen} et al., Optim. Methods Softw. 28, No. 1, 37--53 (2013; Zbl 1264.49031) Full Text: DOI
Hou, TianLiang; Chen, YanPing Superconvergence of RT1 mixed finite element approximations for elliptic control problems. (English) Zbl 1260.49052 Sci. China, Math. 56, No. 2, 267-281 (2013). MSC: 49M25 49M15 49N10 65M25 65M60 PDFBibTeX XMLCite \textit{T. Hou} and \textit{Y. Chen}, Sci. China, Math. 56, No. 2, 267--281 (2013; Zbl 1260.49052) Full Text: DOI
Tang, Yuelong; Chen, Yanping Variational discretization for parabolic optimal control problems with control constraints. (English) Zbl 1269.49054 J. Syst. Sci. Complex. 25, No. 5, 880-895 (2012). MSC: 49M25 49K20 35K20 PDFBibTeX XMLCite \textit{Y. Tang} and \textit{Y. Chen}, J. Syst. Sci. Complex. 25, No. 5, 880--895 (2012; Zbl 1269.49054) Full Text: DOI
Wei, Yunxia; Chen, Yanping Legendre spectral collocation methods for pantograph Volterra delay-integro-differential equations. (English) Zbl 1264.65218 J. Sci. Comput. 53, No. 3, 672-688 (2012). Reviewer: Alexandru Mihai Bica (Oradea) MSC: 65R20 45A05 45D05 45J05 PDFBibTeX XMLCite \textit{Y. Wei} and \textit{Y. Chen}, J. Sci. Comput. 53, No. 3, 672--688 (2012; Zbl 1264.65218) Full Text: DOI
Chen, Yanping; Lu, Zuliang; Guo, Ruyi Error estimates of triangular mixed finite element methods for quasilinear optimal control problems. (English) Zbl 1252.49049 Front. Math. China 7, No. 3, 397-413 (2012). MSC: 49M25 49J20 65N30 35J66 PDFBibTeX XMLCite \textit{Y. Chen} et al., Front. Math. China 7, No. 3, 397--413 (2012; Zbl 1252.49049) Full Text: DOI
Zhou, Qin; Chen, Yanping; Yang, Yin Two improved algorithms and implementation for a singularly perturbed problem on moving meshes. (English) Zbl 1338.93245 J. Syst. Sci. Complex. 24, No. 6, 1232-1240 (2011). MSC: 93C70 65M12 PDFBibTeX XMLCite \textit{Q. Zhou} et al., J. Syst. Sci. Complex. 24, No. 6, 1232--1240 (2011; Zbl 1338.93245) Full Text: DOI
Chen, Yanping; Lin, Yijie A posteriori error estimates for \(hp\) finite element solutions of convex optimal control problems. (English) Zbl 1217.65120 J. Comput. Appl. Math. 235, No. 12, 3435-3454 (2011). Reviewer: Hans Benker (Merseburg) MSC: 65K10 49J20 65N30 PDFBibTeX XMLCite \textit{Y. Chen} and \textit{Y. Lin}, J. Comput. Appl. Math. 235, No. 12, 3435--3454 (2011; Zbl 1217.65120) Full Text: DOI
Chen, Yanping; Liu, Lingli; Lu, Zuliang A posteriori error estimates of mixed methods for parabolic optimal control problems. (English) Zbl 1219.49025 Numer. Funct. Anal. Optim. 31, No. 10, 1135-1157 (2010). MSC: 49M25 65N30 35K20 PDFBibTeX XMLCite \textit{Y. Chen} et al., Numer. Funct. Anal. Optim. 31, No. 10, 1135--1157 (2010; Zbl 1219.49025) Full Text: DOI
Chen, Yanping; Huang, Yunqing; Liu, Wenbin; Yan, Ningning Error estimates and superconvergence of mixed finite element methods for convex optimal control problems. (English) Zbl 1203.49042 J. Sci. Comput. 42, No. 3, 382-403 (2010). MSC: 49M25 65N15 65N30 PDFBibTeX XMLCite \textit{Y. Chen} et al., J. Sci. Comput. 42, No. 3, 382--403 (2010; Zbl 1203.49042) Full Text: DOI
Chen, Yanping; Tang, Tao Convergence analysis of the Jacobi spectral-collocation methods for Volterra integral equations with a weakly singular kernel. (English) Zbl 1207.65157 Math. Comput. 79, No. 269, 147-167 (2010). Reviewer: Ali Filiz (Aydin) MSC: 65R20 45D05 45E10 PDFBibTeX XMLCite \textit{Y. Chen} and \textit{T. Tang}, Math. Comput. 79, No. 269, 147--167 (2010; Zbl 1207.65157) Full Text: DOI
Xing, Xiaoqing; Chen, Yanping; Yi, Nianyu Error estimates of mixed finite element methods for quadratic optimal control problems. (English) Zbl 1181.65096 J. Comput. Appl. Math. 233, No. 8, 1812-1820 (2010). MSC: 65K10 49J20 49M15 PDFBibTeX XMLCite \textit{X. Xing} et al., J. Comput. Appl. Math. 233, No. 8, 1812--1820 (2010; Zbl 1181.65096) Full Text: DOI
Chen, Yanping; Tang, Tao Spectral methods for weakly singular Volterra integral equations with smooth solutions. (English) Zbl 1186.65161 J. Comput. Appl. Math. 233, No. 4, 938-950 (2009). Reviewer: Hu Chuangan (San Jose) MSC: 65R20 45D05 45E10 PDFBibTeX XMLCite \textit{Y. Chen} and \textit{T. Tang}, J. Comput. Appl. Math. 233, No. 4, 938--950 (2009; Zbl 1186.65161) Full Text: DOI
Wan, Zhengsu; Chen, Yanping; Huang, Yunqing Legendre spectral Galerkin method for second-kind Volterra integral equations. (English) Zbl 1396.65165 Front. Math. China 4, No. 1, 181-193 (2009). MSC: 65R20 PDFBibTeX XMLCite \textit{Z. Wan} et al., Front. Math. China 4, No. 1, 181--193 (2009; Zbl 1396.65165) Full Text: DOI
Chen, Yanping Superconvergence of quadratic optimal control problems by triangular mixed finite element methods. (English) Zbl 1195.49038 Int. J. Numer. Methods Eng. 75, No. 8, 881-898 (2008). MSC: 49M25 65K10 PDFBibTeX XMLCite \textit{Y. Chen}, Int. J. Numer. Methods Eng. 75, No. 8, 881--898 (2008; Zbl 1195.49038) Full Text: DOI
Chen, Yanping Superconvergence of mixed finite element methods for optimal control problems. (English) Zbl 1193.49029 Math. Comput. 77, No. 263, 1269-1291 (2008). MSC: 49M15 65N30 PDFBibTeX XMLCite \textit{Y. Chen}, Math. Comput. 77, No. 263, 1269--1291 (2008; Zbl 1193.49029) Full Text: DOI
Chen, YanPing; Huang, YunQing; Yi, NianYu A posteriori error estimates of spectral method for optimal control problems governed by parabolic equations. (English) Zbl 1154.49006 Sci. China, Ser. A 51, No. 8, 1376-1390 (2008). MSC: 49J20 65M60 65M70 35K20 PDFBibTeX XMLCite \textit{Y. Chen} et al., Sci. China, Ser. A 51, No. 8, 1376--1390 (2008; Zbl 1154.49006) Full Text: DOI
Chen, Yanping; Liu, Wenbin A posteriori error estimates for mixed finite element solutions of convex optimal control problems. (English) Zbl 1165.65034 J. Comput. Appl. Math. 211, No. 1, 76-89 (2008). Reviewer: Jan Lovíšek (Bratislava) MSC: 65K10 49J20 65N30 PDFBibTeX XMLCite \textit{Y. Chen} and \textit{W. Liu}, J. Comput. Appl. Math. 211, No. 1, 76--89 (2008; Zbl 1165.65034) Full Text: DOI
Chen, Yanping Uniform convergence analysis of finite difference approximations for singular perturbation problems on an adapted grid. (English) Zbl 1095.65065 Adv. Comput. Math. 24, No. 1-4, 197-212 (2006). MSC: 65L10 65L12 65L20 34E15 65L50 34B05 65L70 PDFBibTeX XMLCite \textit{Y. Chen}, Adv. Comput. Math. 24, No. 1--4, 197--212 (2006; Zbl 1095.65065) Full Text: DOI
Chen, Yanping Uniform pointwise convergence for a singularly perturbed problem using arc-length equidistribution. (English) Zbl 1044.65066 J. Comput. Appl. Math. 159, No. 1, 25-34 (2003). Reviewer: Pavol Chocholatý (Bratislava) MSC: 65L20 65L10 65L12 34B05 34E15 65L50 PDFBibTeX XMLCite \textit{Y. Chen}, J. Comput. Appl. Math. 159, No. 1, 25--34 (2003; Zbl 1044.65066) Full Text: DOI