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A-posteriori error estimation for the finite point method with applications to compressible flow

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Abstract

An a-posteriori error estimate with application to inviscid compressible flow problems is presented. The estimate is a surrogate measure of the discretization error, obtained from an approximation to the truncation terms of the governing equations. This approximation is calculated from the discrete nodal differential residuals using a reconstructed solution field on a modified stencil of points. Both the error estimation methodology and the flow solution scheme are implemented using the Finite Point Method, a meshless technique enabling higher-order approximations and reconstruction procedures on general unstructured discretizations. The performance of the proposed error indicator is studied and applications to adaptive grid refinement are presented.

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Acknowledgements

Part of this work was developed within the ALEF (Aerodynamic Loads Estimation at Extremes of the Flight Envelope) project under the European Commission’s 7th Framework Programme (contract number ACP7-GA-2009-211785). The authors gratefully acknowledge the support provided.

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Authors and Affiliations

  1. Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE), Universitat Politècnica de Catalunya (UPC), 08034, Barcelona, Spain

    Enrique Ortega, Roberto Flores, Eugenio Oñate & Sergio Idelsohn

  2. Institució Catalana de Recerca i Estudis Avançats (ICREA), Barcelona, Spain

    Sergio Idelsohn

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  1. Enrique Ortega
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  2. Roberto Flores
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  3. Eugenio Oñate
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  4. Sergio Idelsohn
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Correspondence to Enrique Ortega.

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Ortega, E., Flores, R., Oñate, E. et al. A-posteriori error estimation for the finite point method with applications to compressible flow. Comput Mech 60, 219–233 (2017). https://doi.org/10.1007/s00466-017-1402-7

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  • DOI: https://doi.org/10.1007/s00466-017-1402-7

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