A posteriori error estimates for fourth order hyperbolic control problems by mixed finite element methods

Abstract

Abstract In this paper, we consider the a posteriori error estimates of the mixed finite element method for the optimal control problems governed by fourth order hyperbolic equations. The state is discretized by the order k Raviart–Thomas mixed elements and control is discretized by piecewise polynomials of degree k. We adopt the mixed elliptic reconstruction to derive the a posteriori error estimates for both the state and the control approximations.

Keywords

• A posteriori error estimates
• Optimal control problems
• Fourth order hyperbolic equations
• Mixed finite element methods