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Application of Variational a-Posteriori Multiscale Error Estimation to Higher-Order Elements

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Abstract

An explicit a-posteriori error estimator based on the variational multiscale method is extended to higher-order elements. The technique is based on a recently derived explicit formula of the fine-scale Green’s function for higher-order elements. For the class of element-edge exact methods, the technique is able to predict the error exactly in any desired norm. It is shown that for elements of order k, the exact error depends on the k−1 derivative of the residual. The technique is applied to one-dimensional examples of fluid transport computed with stabilized methods.

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Authors and Affiliations

  1. Departamento de Mecánica de Fluidos, Centro Politécnico Superior, C/Maria de Luna 3, 50018, Zaragoza, Spain

    Guillermo Hauke, Mohamed H. Doweidar, Daniel Fuster & Antonio Gómez

  2. Departamento de Matemática Aplicada, Centro Politécnico Superior, C/Maria de Luna 3, 50018, Zaragoza, Spain

    Javier Sayas

Authors
  1. Guillermo Hauke
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  2. Mohamed H. Doweidar
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  3. Daniel Fuster
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  4. Antonio Gómez
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  5. Javier Sayas
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Correspondence to Guillermo Hauke.

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Hauke, G., Doweidar, M.H., Fuster, D. et al. Application of Variational a-Posteriori Multiscale Error Estimation to Higher-Order Elements. Comput Mech 38, 382–389 (2006). https://doi.org/10.1007/s00466-006-0048-7

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  • DOI: https://doi.org/10.1007/s00466-006-0048-7

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