Goal-oriented error estimation and adaptivity for the finite element method

By J. Tinsley Oden, Serge Prudhomme. 2001

381 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Electrical and Electronic Engineering

View Paper: https://www.semanticscholar.org/paper/871e3f621ddf2bb33f22969f9bb2e355fd790318

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In Computational Mechanics

In Computational Theory and Mathematics

In Electrical and Electronic Engineering

Citations in the corpus

Review of Output-Based Error Estimation and Mesh Adaptation in Computational Fluid Dynamics (2011, methodology): “The method is also referred to as “goal-oriented” [36,63] or “outputbased” error estimation.”
Strict error bounds for linear solid mechanics problems using a subdomain-based flux-free method (2009, background): “the error in certain quantities of interest, |I (uex)−I (uH )|, but it can be brought back, using a proper error representation [24–29], to that of estimating bounds for the energy norm (for the original problem and a dual one) so that it will not be discussed any further here.”
Convergence, adaptive refinement, and scaling in 1D peridynamics (2009, methodology): “Automatic and goal-oriented h, p, and hp-adaptive strategies for FEM have been introduced and discussed in [3–6].”
The heterogeneous multiscale method* (2012, neutral): “For single-scale problems, such ‘goal-oriented adaptivity’ has been studied in Prudhomme and Oden (1999), Oden and Prudhomme (2001), Becker and Rannacher (2001), Nochetto, Veeser and Verani (2009) and Ainsworth and Rankin (2012).”
Review: A posteriori error estimation techniques in practical finite element analysis (2005, methodology): “For instance, Prud homme and Oden [44,45] employ the parallelogram identity to problems with symmetric bilinear forms lead ing to upper and lower bounds on the error.”
Adaptive reduced basis finite element heterogeneous multiscale method (2013, background): “While there is a large literature for single scale adaptive methods (see for example [15, 16, 17, 18] and the references therein), adaptive multiscale methods are still at an early stage of development.”
Reliability and efficiency of an anisotropic zienkiewicz-zhu error estimator (2006, background): “If linear functionals of eh have to be controlled, dualbased error estimators, involving the solution of a suitable adjoint problem, should be considered [4, 16, 30].”
A Posteriori Error Estimation for Discontinuous Galerkin Approximations of Hyperbolic Systems (2000, neutral): “For an introduction to a posteriori error analysis see Eriksson et al. [9], related work by Estep et al. [13], Parashivoiu et al. [15], and the recent report of Oden and Prudhomme [14].”