Galerkin spectral method for a fourth-order optimal control problem with H1 -norm state constraint

In this article, we are concerned with the Galerkin spectral approximation of an H-1-norm state-constrained optimal control problem governed by a fourth-order partial differential equation (PDE). In the investigations, the optimality conditions for both the original control problem and its spectral approximation problem are, respectively, established, which are helpful to analyze the solution property of the spectral approximation problem. A priori and a posteriori error estimates of the spectral approximation problem are, therewith, built in detail. Finally, two numerical examples are carried out to validate the theoretical analysis.

Automated summary

This article focuses on the Galerkin spectral approximation of an H-1-norm state-constrained optimal control problem governed by a fourth-order partial differential equation (PDE). Optimal conditions for both the original control problem and its spectral approximation problem were established to analyze the solution properties. A priori and a posteriori error estimates of the spectral approximation problem were detailed, with two numerical examples conducted to validate the theoretical analysis.