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Volume 3, Issue 3
Some New Local Error Estimates in Negative Norms with an Application to Local a Posteriori Error Estimation

Alfred H. Schatz

Int. J. Numer. Anal. Mod., 3 (2006), pp. 371-376.

Published online: 2006-03

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  • Abstract

Here we survey some previously published results and announce some that have been newly obtained. We first review some of the results in [3] on estimates for the finite element error at a point. These estimates and analogous ones in [4] and [7] have been applied to problems in a posteriori estimates [2], [8], superconvergence [5] and others [9], [10]. We then discuss the extension of these estimates to local estimates in $L_∞$ based negative norms. These estimates have been newly obtained and are applied to the problem of obtaining an asymptotically exact a posteriori estimator for the maximum norm of the solution error on each element.

  • Keywords

superconvergence, error estimate, a posteriori.

  • AMS Subject Headings

65C30

  • Copyright

COPYRIGHT: © Global Science Press

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  • TXT
@Article{IJNAM-3-371, author = {Schatz , Alfred H.}, title = {Some New Local Error Estimates in Negative Norms with an Application to Local a Posteriori Error Estimation}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2006}, volume = {3}, number = {3}, pages = {371--376}, abstract = {

Here we survey some previously published results and announce some that have been newly obtained. We first review some of the results in [3] on estimates for the finite element error at a point. These estimates and analogous ones in [4] and [7] have been applied to problems in a posteriori estimates [2], [8], superconvergence [5] and others [9], [10]. We then discuss the extension of these estimates to local estimates in $L_∞$ based negative norms. These estimates have been newly obtained and are applied to the problem of obtaining an asymptotically exact a posteriori estimator for the maximum norm of the solution error on each element.

}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/908.html} }
TY - JOUR T1 - Some New Local Error Estimates in Negative Norms with an Application to Local a Posteriori Error Estimation AU - Schatz , Alfred H. JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 371 EP - 376 PY - 2006 DA - 2006/03 SN - 3 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/908.html KW - superconvergence, error estimate, a posteriori. AB -

Here we survey some previously published results and announce some that have been newly obtained. We first review some of the results in [3] on estimates for the finite element error at a point. These estimates and analogous ones in [4] and [7] have been applied to problems in a posteriori estimates [2], [8], superconvergence [5] and others [9], [10]. We then discuss the extension of these estimates to local estimates in $L_∞$ based negative norms. These estimates have been newly obtained and are applied to the problem of obtaining an asymptotically exact a posteriori estimator for the maximum norm of the solution error on each element.

Alfred H. Schatz. (2019). Some New Local Error Estimates in Negative Norms with an Application to Local a Posteriori Error Estimation. International Journal of Numerical Analysis and Modeling. 3 (3). 371-376. doi:
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