An equilibrated fluxes approach to the certified descent algorithm for shape optimization using conforming finite element and discontinuous Galerkin discretizations
CMAP, Inria, Ecole polytechnique, CNRS, Université Paris-Saclay（巴黎萨克雷大学）；DRI Institut Polytechnique des Sciences Avancées（高级科学院理工学院）；Laboratori de Càlcul Numèric, E.T.S. de Ingenieros de Caminos, Universitat Politècnica de Catalunya – BarcelonaTech（加泰罗尼亚理工大学）
The certified descent algorithm (CDA) is a gradient-based method for shape optimization which certifies that the direction computed using the shape gradient is a genuine descent direction for the objective functional under analysis. It relies on the computation of an upper bound of the error introduced by the finite element approximation of the shape gradient. In this paper, we present a goal-oriented error estimator which depends solely on local quantities and is fully-computable. By means of the equilibrated fluxes approach, we construct a unified strategy valid for both conforming finite element approximations and discontinuous Galerkin discretizations. The new variant of the CDA is tested on the inverse identification problem of electrical impedance tomography: both its ability to identify a genuine descent direction at each iteration and its reliable stopping criterion are confirmed.
Robust equilibrated a posteriori error estimators for the Reissner-Mindlin system
Université des Sciences et Technologies de Lille（里尔科学技术大学）；Laboratoire Paul Painlevé UMR 8524（保罗·潘勒韦实验室）；EPI SIMPAF - INRIA Lille Nord Europe（INRIA北欧洲SIMPAF项目组）；Université de Valenciennes et du Hainaut Cambrésis（瓦朗谢讷及康布雷埃斯-哈诺大学）；LAMAV, FR CNRS 2956（拉马夫，法国国家科学研究中心2956）；Institut des Sciences et Techniques de Valenciennes（瓦朗谢讷科学与技术研究所）
$p$-robust equilibrated flux reconstruction in ${\boldsymbol H}(\mathrm{curl})$ based on local minimizations. Application to a posteriori analysis of the curl-curl problem
Numerical analysis of a locking-free primal hybrid method for linear elasticity with $H(\mathrm{div})$-conforming stress recovery
Universidade Estadual de Campinas (Unicamp), Center for Energy and Petroleum Studies（坎皮纳斯州立大学（Unicamp），能源与石油研究中心）；Department of Applied Mathematics, Institute of Mathematics, Statistics and Computer Science, University of São Paulo（圣保罗大学，数学、统计与计算机科学研究所，应用数学系）
On $p$-robust convergence and optimality of adaptive FEM driven by equilibrated-flux estimators
Inria（法国国家数字与工程科学研究所）；Univ. Lille（里尔大学）；Laboratoire Paul Painlevé（保罗·庞加莱实验室）；Inria Paris（法国国家数字与工程科学研究所巴黎分部）；Institute for Numerical Simulation, University of Bonn（波恩大学数值模拟研究所）；University of Twente（特文特大学）；Charles University, Faculty of Mathematics and Physics（查理大学数学物理学院）
Robin Schwarz algorithm for the NICEM Method: the Pq finite element case
Université Paris 13, Sorbonne Paris Cité, LAGA, CNRS UMR 7539（巴黎第十三大学，索邦巴黎城，LAGA，CNRS UMR 7539）；INRIA Paris-Rocquencourt（INRIA 巴黎-罗格库尔中心）；CSCAMM, University of Maryland College Park（马里兰大学学院公园分校 CSCAMM）；UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis Lions（巴黎第六大学，UMR 7598，雅克-路易·利翁斯实验室）；Institut Universitaire de France（法兰西学院）；Brown Univ, Division of Applied Maths（布朗大学应用数学系）；CNRS, UMR 7598, Laboratoire Jacques-Louis Lions（CNRS，UMR 7598，雅克-路易·利翁斯实验室）
A posteriori error estimates and adaptivity for locally conservative methods. Inexpensive implementation and evaluation, polytopal meshes, iterative linearization and algebraic solvers, and applications to complex porous media flows
Adaptive asynchronous time-stepping, stopping criteria, and a posteriori error estimates for fixed-stress iterative schemes for coupled poromechanics problems
Guaranteed, locally space-time efficient, and polynomial-degree robust a posteriori error estimates for high-order discretizations of parabolic problems
