Mallik, G (2022) Goal-oriented a posteriori error estimation for the biharmonic problem based on an equilibrated moment tensor. In: Computers and Mathematics with Applications, 117 . pp. 312-325.
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Abstract
In this article, we discuss goal-oriented a posteriori error estimation for the biharmonic plate bending problem. The error for a numerical approximation of a goal functional is represented by several computable estimators. One of these estimators is obtained using the dual-weighted residual method, which takes advantage of an equilibrated moment tensor. Then, an abstract unified framework for the goal-oriented a posteriori error estimation is derived based on the equilibrated moment tensor and the potential reconstruction that provides a guaranteed upper bound for the error of a numerical approximation for the goal functional. In particular, C0 interior penalty and discontinuous Galerkin finite element methods are employed for the practical realisation of the estimators. Numerical experiments are performed to illustrate the effectivity of the estimators.
| Item Type: | Journal Article |
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| Publication: | Computers and Mathematics with Applications |
| Publisher: | Elsevier Ltd |
| Additional Information: | The copyright for this article belongs to the Author(s). |
| Keywords: | Error analysis; Galerkin methods; Tensors, A-posteriori error estimates; Adaptivity; Biharmonic problem; Equilibrated moment tensor; Goal-oriented a posteriori error estimations; Guaranteed bounds; Moment tensors; Numerical approximations; Quantity of interest; Unified framework, Abstracting |
| Department/Centre: | Division of Physical & Mathematical Sciences > Mathematics |
| Date Deposited: | 19 Sep 2022 10:14 |
| Last Modified: | 19 Sep 2022 10:14 |
| URI: | https://eprints.iisc.ac.in/id/eprint/76609 |
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