A Posteriori Error Estimation in Finite Element Analysis

By Mark Ainsworth, J. Tinsley Oden. 2000

2,932 citations recorded by the source corpus.

Subfields: Civil and Structural Engineering, Mechanical Engineering

View Paper: https://www.semanticscholar.org/paper/29ce39af7c335efd241fb6f7908367a706d881c0

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In Civil and Structural Engineering

In Mechanical Engineering

Citations in the corpus

Adaptive stochastic Galerkin FEM (2014, background): “5) following the standard argument from [20, 1, 23], see also [14].”
A comprehensive framework for verification, validation, and uncertainty quantification in scientific computing (2011, methodology): “The Type II methods employ additional information about the problem being solved and include discretization error transport equations [20,21], defect correction methods [22], and implicit/explicit residual methods in finite elements [23,24].”
Goal functional evaluations for phase-field fracture using PU-based DWR mesh adaptivity (2016, background): “Important further developments in the early stages have been accomplished in [1,43,42,28,21,9].”
Hybridizable Discontinuous Galerkin with degree adaptivity for the incompressible Navier-Stokes equations ✩ (2014, neutral): “Error estimation and degree adaptive algorithm The use of a posteriori computable error estimates to drive an automatic adaptive process is nowadays a common practice to control the accuracy of the computation and to ensure the quality of the FE solution [33].”
An Isogeometric design-through-analysis methodology based on adaptive hierarchical refinement of NURBS, immersed boundary methods, and T-spline CAD surfaces (2012, background): “For more elaborate error estimators, see for example [72].”
An error estimator for separated representations of highly multidimensional models (2010, methodology): “Thus, we can define a conductivity varying in the interval [0, 1], where the highest values were depicted in red in figure 6 and the regions with lowest conductivity were represented in blue.”
A recovery‐type error estimator for the extended finite element method based on singular+smooth stress field splitting (2008, methodology): “The error assessment tools used in finite element analysis are well known and are usually classified [9,10] into two families: residual-type error estimators and recovery-based error estimators.”
A review of unified a posteriori finite element error control (2012, neutral): “[1,8,43].”
An accurate H(div) flux reconstruction for discontinuous Galerkin approximations of elliptic problems (2007, methodology): “For conforming approximations, this type of estimates are explored, e.g., in [ 1 ,10] and references therein.”
Discontinuous Galerkin methods for reactive transport in porous media (2003, methodology): “A posteriori error estimators can be used to signify where modifications in discretization parameters need to be made and thus to achieve adaptivity, in particular the goal-oriented hp-adaptivity [1– 4, 21, 28–30, 32–34, 51, 58, 61, 64, 67–69, 86], see also [5, 12, 96] and references therein.”
A robust SUPG norm a posteriori error estimator for stationary convection-diffusion equations (2013, background): “All effectivity indices are in the interval [1,8], but there is some increase on finer levels.”
Reduced Basis Approximation and a Posteriori Error Estimation for Affinely Parametrized Elliptic Coercive Partial Differential Equations (2007, positive): “In Section 9 we present rigorous and relatively sharp a posteriori output error bounds [ 3 ,23,108] for RB approximations [121,142]; in Section 10 we develop the coercivity-constant lower bounds [64] required by the a posteriori error estimation procedures.”
Adaptive Finite Element Methods for Optimal Control of Partial Differential Equations: Basic Concept (2000, methodology): “For a discussion of adaptive finite element methods using residual-based a posteriori error estimates, we refer to the survey papers [1], [14], [8], and [12].”
Numerical partial differential equations for environmental scientists and engineers (2013, background): “If [Cov(b)] = a2 [I], then [Cov (d)] = a2 [I] and”
A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data (2007, methodology): “Some sources of errors arising in computer simulations now can be controlled and reduced by using sophisticated techniques such as a posteriori error estimation [1, 3, 57], mesh adaptivity, and the more recent modeling error analysis [49, 50, 13].”