@Article{CiCP-7-3,
author = {},
title = {On the Use of Adjoint-Based Sensitivity Estimates to Control Local Mesh Refinement},
journal = {Communications in Computational Physics},
year = {2010},
volume = {7},
number = {3},
pages = {631--638},
abstract = {<p style="text-align: justify;">The goal of efficient and robust error control, through local mesh adaptation
in the computational solution of partial differential equations, is predicated on the
ability to identify in an a posteriori way those localized regions whose refinement will
lead to the most significant reductions in the error. The development of a posteriori error
estimation schemes and of a refinement infrastructure both facilitate this goal, however
they are incomplete in the sense that they do not provide an answer as to where the
maximal impact of refinement may be gained or what type of refinement — elemental
partitioning (h-refinement) or polynomial enrichment (p-refinement) — will best lead
to that gain. In essence, one also requires knowledge of the sensitivity of the error to
both the location and the type of refinement. In this communication we propose the
use of adjoint-based sensitivity analysis to discriminate both where and how to refine.
We present both an adjoint-based and an algebraic perspective on defining and using
sensitivities, and then demonstrate through several one-dimensional model problem
experiments the feasibility and benefits of our approach.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.2009.09.060},
url = {https://global-sci.com/article/80998/on-the-use-of-adjoint-based-sensitivity-estimates-to-control-local-mesh-refinement}
}