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Volume 10, Issue 2
Hierarchical a Posteriori Residual Based Error Estimators for Bilinear Finite Elements

M. Braack & N. Taschenberger

Int. J. Numer. Anal. Mod., 10 (2013), pp. 466-480.

Published online: 2013-10

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  • Abstract

We present techniques of a posteriori error estimation for $Q_1$ finite element discretizations based on residual evaluations with respect to test functions of higher-order. This technique is designed for quadrilateral (or hexahedral) triangulations and gives local error indicators in terms of nodal contributions. We show reliability and efficiency of the estimator. Moreover, we present a simplification which is attractive from computational point of view as well.

  • Keywords

error estimates, adaptivity, finite elements.

  • AMS Subject Headings

65N15, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-10-466, author = {M. Braack and N. Taschenberger}, title = {Hierarchical a Posteriori Residual Based Error Estimators for Bilinear Finite Elements}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2013}, volume = {10}, number = {2}, pages = {466--480}, abstract = {

We present techniques of a posteriori error estimation for $Q_1$ finite element discretizations based on residual evaluations with respect to test functions of higher-order. This technique is designed for quadrilateral (or hexahedral) triangulations and gives local error indicators in terms of nodal contributions. We show reliability and efficiency of the estimator. Moreover, we present a simplification which is attractive from computational point of view as well.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/578.html} }
TY - JOUR T1 - Hierarchical a Posteriori Residual Based Error Estimators for Bilinear Finite Elements AU - M. Braack & N. Taschenberger JO - International Journal of Numerical Analysis and Modeling VL - 2 SP - 466 EP - 480 PY - 2013 DA - 2013/10 SN - 10 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/578.html KW - error estimates, adaptivity, finite elements. AB -

We present techniques of a posteriori error estimation for $Q_1$ finite element discretizations based on residual evaluations with respect to test functions of higher-order. This technique is designed for quadrilateral (or hexahedral) triangulations and gives local error indicators in terms of nodal contributions. We show reliability and efficiency of the estimator. Moreover, we present a simplification which is attractive from computational point of view as well.

M. Braack and N. Taschenberger. (2013). Hierarchical a Posteriori Residual Based Error Estimators for Bilinear Finite Elements. International Journal of Numerical Analysis and Modeling. 10 (2). 466-480. doi:
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