Modified C0 interior penalty analysis for fourth order Dirichlet boundary control problem and a posteriori error estimate

TL;DR

This paper improves error estimates for a fourth order boundary control problem using C0 interior penalty methods, applicable to convex polygons, with reliable residual-based a posteriori error bounds demonstrated through numerical tests.

Contribution

It provides a new L2 norm error estimate under reduced regularity assumptions and develops reliable, efficient residual-based a posteriori error bounds for the control, state, and adjoint variables.

Findings

L2 error estimate derived under minimal regularity

Residual-based a posteriori error bounds established

Numerical experiments confirm theoretical results

Abstract

We revisit the L2 norm error estimate for the C0 interior penalty analysis of fourth order Dirichlet boundary control problem. The L2 norm estimate for the optimal control is derived under reduced regularity assumption and this analysis can be carried out on any convex polygonal domains. Residual based a-posteriori error bounds are derived for optimal control, state and adjoint state variables under minimal regularity assumptions. The estimators are shown to be reliable and locally efficient. The theoretical findings are illustrated by numerical experiments.