TY - JOUR
T1 - A new goal-oriented formulation of the finite element method
AU - Kergrene, Kenan
AU - Prudhomme, Serge
AU - Chamoin, Ludovic
AU - Laforest, Marc
N1 - KAUST Repository Item: Exported on 2021-04-06
Acknowledged KAUST grant number(s): CRG3, OCRF-2014-CRG
Acknowledgements: SP is grateful for the support by a Discovery Grant from the Natural Sciences and Engineering Research Council of Canada. He also acknowledges the support by KAUST under Award Number OCRF-2014-CRG3-2281. Moreover, the authors gratefully acknowledge Jonathan Vacher for fruitful discussions on the subject.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.
PY - 2017/12
Y1 - 2017/12
N2 - In this paper, we introduce, analyze, and numerically illustrate a method for taking into account quantities of interest during the finite element treatment of a boundary-value problem. The objective is to derive a method whose computational cost is of the same order as that of the classical approach for goal-oriented adaptivity, which involves the solution of the primal problem and of an adjoint problem used to weigh the residual and provide indicators for mesh refinement. In the current approach, we first solve the adjoint problem, then use the adjoint information as a minimization constraint for the primal problem. As a result, the constrained finite element solution is enhanced with respect to the quantities of interest, while maintaining near-optimality in energy norm. We describe the formulation in the case of a problem defined by a symmetric continuous coercive bilinear form and demonstrate the efficiency of the new approach on several numerical examples.
AB - In this paper, we introduce, analyze, and numerically illustrate a method for taking into account quantities of interest during the finite element treatment of a boundary-value problem. The objective is to derive a method whose computational cost is of the same order as that of the classical approach for goal-oriented adaptivity, which involves the solution of the primal problem and of an adjoint problem used to weigh the residual and provide indicators for mesh refinement. In the current approach, we first solve the adjoint problem, then use the adjoint information as a minimization constraint for the primal problem. As a result, the constrained finite element solution is enhanced with respect to the quantities of interest, while maintaining near-optimality in energy norm. We describe the formulation in the case of a problem defined by a symmetric continuous coercive bilinear form and demonstrate the efficiency of the new approach on several numerical examples.
UR - http://hdl.handle.net/10754/668553
UR - https://linkinghub.elsevier.com/retrieve/pii/S0045782517306485
UR - http://www.scopus.com/inward/record.url?scp=85031423347&partnerID=8YFLogxK
U2 - 10.1016/j.cma.2017.09.018
DO - 10.1016/j.cma.2017.09.018
M3 - Article
SN - 0045-7825
VL - 327
SP - 256
EP - 276
JO - Computer Methods in Applied Mechanics and Engineering
JF - Computer Methods in Applied Mechanics and Engineering
ER -