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Error estimates of finite element methods for parameter identifications in elliptic and parabolic systems
1. | Department of Mathematics, Wuhan University, Wuhan 430072, China |
2. | Department of Mathematics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong |
[1] |
Vinicius Albani, Adriano De Cezaro, Jorge P. Zubelli. On the choice of the Tikhonov regularization parameter and the discretization level: A discrepancy-based strategy. Inverse Problems & Imaging, 2016, 10 (1) : 1-25. doi: 10.3934/ipi.2016.10.1 |
[2] |
J. Mead. $ \chi^2 $ test for total variation regularization parameter selection. Inverse Problems & Imaging, 2020, 14 (3) : 401-421. doi: 10.3934/ipi.2020019 |
[3] |
Alina Toma, Bruno Sixou, Françoise Peyrin. Iterative choice of the optimal regularization parameter in TV image restoration. Inverse Problems & Imaging, 2015, 9 (4) : 1171-1191. doi: 10.3934/ipi.2015.9.1171 |
[4] |
You-Wei Wen, Raymond Honfu Chan. Using generalized cross validation to select regularization parameter for total variation regularization problems. Inverse Problems & Imaging, 2018, 12 (5) : 1103-1120. doi: 10.3934/ipi.2018046 |
[5] |
Liupeng Wang, Yunqing Huang. Error estimates for second-order SAV finite element method to phase field crystal model. Electronic Research Archive, 2021, 29 (1) : 1735-1752. doi: 10.3934/era.2020089 |
[6] |
Thorsten Hohage, Mihaela Pricop. Nonlinear Tikhonov regularization in Hilbert scales for inverse boundary value problems with random noise. Inverse Problems & Imaging, 2008, 2 (2) : 271-290. doi: 10.3934/ipi.2008.2.271 |
[7] |
Qinqin Chai, Ryan Loxton, Kok Lay Teo, Chunhua Yang. A unified parameter identification method for nonlinear time-delay systems. Journal of Industrial & Management Optimization, 2013, 9 (2) : 471-486. doi: 10.3934/jimo.2013.9.471 |
[8] |
Andreas Neubauer. On Tikhonov-type regularization with approximated penalty terms. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2021027 |
[9] |
Stefan Kindermann, Andreas Neubauer. On the convergence of the quasioptimality criterion for (iterated) Tikhonov regularization. Inverse Problems & Imaging, 2008, 2 (2) : 291-299. doi: 10.3934/ipi.2008.2.291 |
[10] |
Jie Shen, Xiaofeng Yang. Error estimates for finite element approximations of consistent splitting schemes for incompressible flows. Discrete & Continuous Dynamical Systems - B, 2007, 8 (3) : 663-676. doi: 10.3934/dcdsb.2007.8.663 |
[11] |
Ole Løseth Elvetun, Bjørn Fredrik Nielsen. A regularization operator for source identification for elliptic PDEs. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2021006 |
[12] |
Abhishake Rastogi. Tikhonov regularization with oversmoothing penalty for nonlinear statistical inverse problems. Communications on Pure & Applied Analysis, 2020, 19 (8) : 4111-4126. doi: 10.3934/cpaa.2020183 |
[13] |
Xianbo Sun, Zhanbo Chen, Pei Yu. Parameter identification on Abelian integrals to achieve Chebyshev property. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020375 |
[14] |
Pingping Niu, Shuai Lu, Jin Cheng. On periodic parameter identification in stochastic differential equations. Inverse Problems & Imaging, 2019, 13 (3) : 513-543. doi: 10.3934/ipi.2019025 |
[15] |
Yuepeng Wang, Yue Cheng, I. Michael Navon, Yuanhong Guan. Parameter identification techniques applied to an environmental pollution model. Journal of Industrial & Management Optimization, 2018, 14 (2) : 817-831. doi: 10.3934/jimo.2017077 |
[16] |
Dominik Hafemeyer, Florian Mannel, Ira Neitzel, Boris Vexler. Finite element error estimates for one-dimensional elliptic optimal control by BV-functions. Mathematical Control & Related Fields, 2020, 10 (2) : 333-363. doi: 10.3934/mcrf.2019041 |
[17] |
Zhenlin Guo, Ping Lin, Guangrong Ji, Yangfan Wang. Retinal vessel segmentation using a finite element based binary level set method. Inverse Problems & Imaging, 2014, 8 (2) : 459-473. doi: 10.3934/ipi.2014.8.459 |
[18] |
Xiaoli Lu, Pengzhan Huang, Yinnian He. Fully discrete finite element approximation of the 2D/3D unsteady incompressible magnetohydrodynamic-Voigt regularization flows. Discrete & Continuous Dynamical Systems - B, 2021, 26 (2) : 815-845. doi: 10.3934/dcdsb.2020143 |
[19] |
Marita Holtmannspötter, Arnd Rösch, Boris Vexler. A priori error estimates for the space-time finite element discretization of an optimal control problem governed by a coupled linear PDE-ODE system. Mathematical Control & Related Fields, 2021 doi: 10.3934/mcrf.2021014 |
[20] |
Barbara Kaltenbacher, William Rundell. On the identification of the nonlinearity parameter in the Westervelt equation from boundary measurements. Inverse Problems & Imaging, , () : -. doi: 10.3934/ipi.2021020 |
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