A priori error estimates and superconvergence of splitting positive definite mixed finite element methods for pseudo-hyperbolic integro-differential optimal control problems
C. Xu
School of Mathematics and Statistics, Beihua University, Jilin, China
Keywords: псевдогиперболические интегро-дифференциальные уравнения, задачи оптимального управления, априорные оценки ошибки, сверхсходимость, положительно определенные смешанные методы расщепления конечных элементов, pseudo-hyperbolic integro-differential equations, optimal control problems, a priori error estimates, superconvergence, splitting positive definite mixed finite element methods
Abstract
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.
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