Review: A posteriori error estimation techniques in practical finite element analysis

By T. Grätsch, Klaus-Jürgen Bathe. 2005

212 citations recorded by the source corpus.

In this paper we review the basic concepts to obtain a posteriori error estimates for the finite element solution of an elliptic linear model problem. We give the basic ideas to establish global error estimates for the energy norm as well as goal-oriented error estimates. While we show how these error estimation techniques are employed for our simple model problem, the emphasis of the paper is on assessing whether these procedures are ready for use in practical linear finite element analysis. We conclude that the actually practical error estimation techniques do not provide mathematically proven bounds on the error and need to be used with care. The more accurate estimation procedures also do not provide proven bounds that, in general, can be computed efficiently. We also briefly comment upon the state of error estimations in nonlinear and transient analyses and when mixed methods are used.

Subfields: Computational Mechanics, Electrical and Electronic Engineering, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/979712905004393ce9637f7839219c3e957d48f3

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In Computational Mechanics

  1. Seounghyun Ham
  2. Klaus-Jürgen Bathe
  3. Gunwoo Noh
  4. Phill-Seung Lee
  5. Suvranu De
  6. Laura De Lorenzis
  7. Giorgio Zavarise
  8. Hou Zhang

In Electrical and Electronic Engineering

  1. Seounghyun Ham
  2. Klaus-Jürgen Bathe
  3. Gunwoo Noh
  4. Jie Zhang
  5. Donghuan Liu
  6. Yinghua Liu
  7. Suvranu De
  8. Laura De Lorenzis

In Mechanics of Materials

  1. Seounghyun Ham
  2. Klaus-Jürgen Bathe
  3. Gunwoo Noh
  4. Suvranu De
  5. Yuantong T. Gu
  6. Elyas Shivanian
  7. Guirong Liu
  8. Jens Markus Melenk

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