Goal-Oriented A Posteriori Error Estimation for the Biharmonic Problem Based on Equilibrated Moment Tensor

TL;DR

This paper develops a goal-oriented a posteriori error estimator for the biharmonic problem using equilibrated moment tensors, combining dual-weighted residuals and finite element methods for guaranteed error bounds.

Contribution

It introduces a unified framework for goal-oriented error estimation in biharmonic problems utilizing equilibrated moment tensors and potential reconstruction.

Findings

Estimator provides guaranteed upper bounds for goal errors.

Numerical experiments confirm the effectiveness of the proposed estimators.

Applicable to $C^0$ interior penalty and discontinuous Galerkin methods.

Abstract

In this article, goal-oriented a posteriori error estimation for the biharmonic plate bending problem is considered. The error for approximation of goal functional is represented by an estimator which combines dual-weighted residual method and equilibrated moment tensor. An abstract unified framework for the goal-oriented a posteriori error estimation is derived. In particular, $C^0$ interior penalty and discontinuous Galerkin finite element methods are employed for practical realization. The abstract estimation is based on equilibrated moment tensor and potential reconstruction that provides a guaranteed upper bound for the goal error. Numerical experiments are performed to illustrate the effectivity of the estimators.