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

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.