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Volume 2, Issue 1
A Posteriori Error Estimation for Non-Conforming Quadrilateral Finite Elements

Mark Ainsworth

Int. J. Numer. Anal. Mod., 2 (2005), pp. 1-18.

Published online: 2005-02

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  • Abstract

We derive an a posteriori error estimator giving a computable upper bound on the error in the energy norm for finite element approximation using the non-conforming rotated $\mathbb{Q}_1$ finite element. It is shown that the estimator also gives a local lower bound up to a generic constant. The bounds do not require additional assumptions on the regularity of the true solution of the underlying elliptic problem and, the mesh is only required to be locally quasi-uniform and may consist of general, non-affine convex quadrilateral elements.

  • Keywords

a posteriori error estimation, non-conforming finite elements, rotated $\mathbb{Q}_1$ element, non-affine quadrilateral elements.

  • AMS Subject Headings

65N50, 65N15, 65N50, 76S05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{IJNAM-2-1, author = {Ainsworth , Mark}, title = {A Posteriori Error Estimation for Non-Conforming Quadrilateral Finite Elements}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2005}, volume = {2}, number = {1}, pages = {1--18}, abstract = {

We derive an a posteriori error estimator giving a computable upper bound on the error in the energy norm for finite element approximation using the non-conforming rotated $\mathbb{Q}_1$ finite element. It is shown that the estimator also gives a local lower bound up to a generic constant. The bounds do not require additional assumptions on the regularity of the true solution of the underlying elliptic problem and, the mesh is only required to be locally quasi-uniform and may consist of general, non-affine convex quadrilateral elements.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/916.html} }
TY - JOUR T1 - A Posteriori Error Estimation for Non-Conforming Quadrilateral Finite Elements AU - Ainsworth , Mark JO - International Journal of Numerical Analysis and Modeling VL - 1 SP - 1 EP - 18 PY - 2005 DA - 2005/02 SN - 2 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/916.html KW - a posteriori error estimation, non-conforming finite elements, rotated $\mathbb{Q}_1$ element, non-affine quadrilateral elements. AB -

We derive an a posteriori error estimator giving a computable upper bound on the error in the energy norm for finite element approximation using the non-conforming rotated $\mathbb{Q}_1$ finite element. It is shown that the estimator also gives a local lower bound up to a generic constant. The bounds do not require additional assumptions on the regularity of the true solution of the underlying elliptic problem and, the mesh is only required to be locally quasi-uniform and may consist of general, non-affine convex quadrilateral elements.

Ainsworth , Mark. (2005). A Posteriori Error Estimation for Non-Conforming Quadrilateral Finite Elements. International Journal of Numerical Analysis and Modeling. 2 (1). 1-18. doi:
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