Adjoint methods for PDEs: a posteriori error analysis and postprocessing by duality

By M. Giles, Endre Süli. Acta Numerica, 2002

546 citations recorded by the source corpus.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/dd317e653500ab3600caa16acfde0e39be461d65

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In Computational Mechanics

In Electrical and Electronic Engineering

In Numerical Analysis

Citations in the corpus

Adaptive Finite Element Approximation of Hyperbolic Problems (2003, unknown): “Example 1: Convergen e of the terms in the error representation formula (22) with Æ = h=4, and the rate of onvergen e k Mesh I1;Æ k II1;Æ k III1;Æ k 17 17 4:396 10 6 - 1:400 10 5 - 2:447 10 4 33 33 2:980 10 7 3:88 2:130 10 6 2:72 3:339 10 5 2:87 65 65 1:951 10 8 3:93 2:748 10 7 2:95 4:378 10 6 2:93 ”
p-Multigrid solution of high-order discontinuous Galerkin discretizations of the compressible Navier-Stokes equations (2005, background): “While it is not clear why the p = 3 rate degrades for the second refinement, it is possible that superconvergent results should be expected for the drag error in this case [28].”
Review of Output-Based Error Estimation and Mesh Adaptation in Computational Fluid Dynamics (2011, methodology): “In addition, Giles and Pierce [15] [16] describe adjoint correction techniques and Giles and Süli [17] review a posteriori output-error estimation for finite element methods applied to linear and nonlinear partial differential equations relevant to CFD. Hartmann and Houston also provide a recent ove”
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].”
Effective adjoint approaches for computational fluid dynamics (2019, methodology): “The adjoint method has also been used in topology optimization for flows [33, 91–93] and structures [94, 95], as well as for error estimation [96–98], uncertainty quantification [96, 99, 100], and inverse designs [48, 101, 102].”
Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book (2012, methodology): “3 is determined by a modified Gillespie method (Gillespie, 1977), which resembles one presented in Rüdiger et al. (2007). Here we will not go into detail, but rather focus on the part of the method that has importance for the overall time stepping algorithm.”
A review of numerical methods for nonlinear partial differential equations (2012, unknown): “To overcome the lack of smoothness, one can use negative Sobolev norms |(cid:7)·|(cid:7) W − m ( L p ) [151, 196, 85].”
Numerical error estimation for nonlinear hyperbolic PDEs via nonlinear error transport (2011, methodology): “Adjoint methods [7, 8] estimate the error in a QoI from the solution of an auxiliary adjoint problem and the residual of the discrete solution.”
Space--time discontinuous Galerkin finite element method with dynamic grid motion for inviscid compressible flows: I. general formulation (2002, background): “This has only been done for target functionals of the data, such as lift and drag on an airfoil (for a survey, see Giles and Süli [15]), but this does not provide a global error estimate for the solution.”