Fully discrete P02−P1 mixed elements for optimal control with parabolic equations and low regularity

Abstract

This paper studies a novel fully discrete mixed method for optimal control problems (OCPs) with parabolic equations and low regularity. The backward difference scheme and $P_0^2-P_1$ mixed finite elements (MFEs) are used for temporal and spatial discretization of state and adjoint state, respectively. Error estimates of all variables are derived through the introduction of specific auxiliary variables and the application of suitable regularity assumptions. The theoretical analysis is validated by two numerical examples.