A posteriori error estimation in finite element analysis

By Stefano de Miranda, Francesco Ubertini. 2004

216 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/9d4c5252fe6a837b0f579b04b99b9a5464da1972

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Citations in the corpus

Automated Solution of Differential Equations by the Finite Element Method: The FEniCS Book (2012, background): “(1998); Ainsworth and Oden (1993) and the reviews papers (Eriksson et al., 1995; Verfürth, 1994, 1999; Ainsworth and Oden, 2000; Becker and Rannacher, 2001).”
Grid adaptation for functional outputs: application to two-dimensional inviscid flows (2002, background): “Even within the setting of finiteelement-discretized elliptic problems, where rigorous and robust error estimators have been available for decades [ 1 , 16, 20], one can argue that a global error norm based directly on the solution and its derivaties may not be optimal within an engineering context.”
Measures of agreement between computation and experiment: Validation metrics (2004, unknown): “[5,10–14] for further discussion of numerical error estimation.”
Shape optimization with a level set based mesh evolution method (2014, unknown): “on a posteriori error estimates for finite element methods [1], could be aimed at getting a sharper resolution of the linearized elasticity system involved in the computation of a descent direction for the given objective functional.”
Verification and Validation in Computational Fluid Dynamics (2002, unknown): “A recent review of the important role of a posteriori estimates in adaptivity for finite elements is the paper by Ainsworth and Oden [14].”
Advances in Studies and Applications of Centroidal Voronoi Tessellations (2010, background): “Adaptive finite element and finite volume methods for the numerical solution of PDEs have been well developed in the past decades [4, 90].”
Anisotropic and dynamic mesh adaptation for discontinuous Galerkin methods applied to reactive transport (2006, background): “The reader is referred to [2,8,9,15,26] for further information.”
Review: A posteriori error estimation techniques in practical finite element analysis (2005, background): “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.”