Shahid Rajaee Teacher Training University (SRTTU) Journal of Computational & Applied Research in Mechanical Engineering (JCARME) 2228-7922 1 1 2011 09 11 Variational discretization and mixed methods for semilinear parabolic optimal control problems with integral constraint 29 36 1 10.22061/jcarme.2011.1 EN Zuliang Lu* School of Mathematics and Statistics, Chongqing Three Gorges University, Chongqing 404000, P.R.China; College of Civil Engineering and Mechanics, Xiangtan University, Xiangtan 411105, P.R.China College of Civil Engineering and Mechanics, Xiangtan University, Xiangtan 411105, P.R.China Journal Article 2011 06 30 The aim of this work is to investigate the variational discretization and mixed finite element methods for optimal control problem governed by semi linear parabolic equations with integral constraint. The state and co-state are approximated by the lowest order Raviart-Thomas mixed finite element spaces and the control is not discreted. Optimal error estimates in L² are established for the state and the control variable. As a result, it can be proved that the discrete solutions possess the convergence property of order. Finally, a numerical example is presented which confirms the theoretical results. https://jcarme.sru.ac.ir/article_1_ad25c41273e42c6a73b0abe8761bfc39.pdf