A priori error estimates of finite volume methods for general elliptic optimal control problems
Texas State University, Department of Mathematics
In this article, we establish a priori error estimates for the finite volume approximation of general elliptic optimal control problems. We use finite volume methods to discretize the state and adjoint equation of the optimal control problems. For the variational inequality, we use the variational discretization methods to discretize the control. We show the existence and the uniqueness of the solution for discrete optimality conditions. Under some reasonable assumptions, we obtain some optimal order error estimates for the state, costate and control variables. On one hand, the convergence rate for the state, costate and control variables is O(h2) or O(h2 √|log(1/h)|) in the sense of L2 norm or L∞ norm. On the other hand, the convergence rate for the state and costate variables is O(h) or O(h|log(1/h)|) in the sense of H1 norm or W1,∞ norm.
A priori error estimates, General elliptic optimal control problems, Finite volume methods, Optimal-order
Feng, Y., Lu, Z., Cao, L., Li, L., & Zhang, S. (2017). A priori error estimates of finite volume methods for general elliptic optimal control problems. <i>Electronic Journal of Differential Equations, 2017</i>(267), pp. 1-15.