Geodesic
A priori error estimates and superconvergence of splitting positive definite mixed finite element methods for pseudo-hyperbolic integro-differential optimal control problems
Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 23 (2020) no. 1, pp. 23-37

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In this paper, we discuss a priori error estimates and superconvergence of splitting positive definite mixed finite element methods for optimal control problems governed by pseudo-hyperbolic integro-differential equations. The state variables and co-state variables are approximated by the lowest order Raviart–Thomas mixed finite element functions, and the control variable is approximated by piecewise constant functions. First, we derive a priori error estimates both for the control variable, the state variables and the co-state variables. Second, we obtain a superconvergence result for the control variable. 
@article{SJVM_2020_23_1_a1,
     author = {C. Xu},
     title = {A priori error estimates and superconvergence of splitting positive definite mixed finite element methods for pseudo-hyperbolic integro-differential optimal control problems},
     journal = {Sibirskij \v{z}urnal vy\v{c}islitelʹnoj matematiki},
     pages = {23--37},
     publisher = {mathdoc},
     volume = {23},
     number = {1},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJVM_2020_23_1_a1/}
}
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C. Xu. A priori error estimates and superconvergence of splitting positive definite mixed finite element methods for pseudo-hyperbolic integro-differential optimal control problems. Sibirskij žurnal vyčislitelʹnoj matematiki, Tome 23 (2020) no. 1, pp. 23-37. http://geodesic.mathdoc.fr/item/SJVM_2020_23_1_a1/