An A Posteriori Analysis of C^0 Interior Penalty Methods for the Obstacle Problem of Clamped Kirchhoff Plates

TL;DR

This paper develops an a posteriori error analysis and adaptive algorithm for C^0 interior penalty methods applied to the obstacle problem of clamped Kirchhoff plates, demonstrating optimal performance through numerical experiments.

Contribution

It extends residual-based error estimators to obstacle problems and establishes their reliability and efficiency for adaptive methods in this context.

Findings

Error estimator is reliable and efficient for obstacle problems.

Adaptive algorithm achieves optimal performance.

Numerical results confirm effectiveness for quadratic and cubic methods.

Abstract

We develop an a posteriori analysis of C^0 interior penalty methods for the displacement obstacle problem of clamped Kirchhoff plates. We show that a residual based error estimator originally designed for C^0 interior penalty methods for the boundary value problem of clamped Kirchhoff plates can also be used for the obstacle problem. We obtain reliability and efficiency estimates for the error estimator and introduce an adaptive algorithm based on this error estimator. Numerical results indicate that the performance of the adaptive algorithm is optimal for both quadratic and cubic C^0 interior penalty methods.