Superconvergence of Semidiscrete Splitting Positive Definite Mixed Finite Elements for Hyperbolic Optimal Control Problems

In this paper, we consider semidiscrete splitting positive definite mixed finite element methods for optimal control problems governed by hyperbolic equations with integral constraints. The state and costate are approximated by the lowest order Raviart-Thomas mixed rectangular finite element, and the control is approximated by piecewise constant functions. We derive some convergence and superconvergence results for the control, the state and the adjoint state. A numerical example is provided to demonstrate our theoretical results.

A posteriori error estimates based on superconvergence of FEM for fractional evolution equations

In this paper, we consider an approximation scheme for fractional evolution equation with variable coefficient. The space derivative is approximated by triangular finite element and the time fractional derivative is evaluated by the L1 approximation. The main aim of this work is to provide convergence and superconvergence analysis and derive a posteriori error estimates. Some numerical examples are presented to demonstrate our theoretical results.

Adaptive variational discretization approximation method for parabolic optimal control problems

In this paper, we study variational discretization method for parabolic optimization problems. Firstly, we obtain some convergence and superconvergence analysis results of the approximation scheme. Secondly, we derive a posteriori error estimates of the approximation solutions. Finally, we present variational discretization approximation algorithm and adaptive variational discretization approximation algorithm for parabolic optimization problems and do some numerical experiments to confirm our theoretical results.