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STABILIZED, MULTISCALE, AND MULTIPHYSICS METHODS IN FLUID MECHANICS

Variational Multiscale A Posteriori Error Estimation for Quantities of Interest

[+] Author and Article Information
Guillermo Hauke

 LITEC (CSIC) – Area de Mecanica de Fluidos, Centro Politecnico Superior Zaragoza, C/Maria de Luna 3, 50018 Zaragoza, Spainghauke@unizar.es

Daniel Fuster

 LITEC (CSIC) – Area de Mecanica de Fluidos, Centro Politecnico Superior Zaragoza, C/Maria de Luna 3, 50018 Zaragoza, Spain

J. Appl. Mech 76(2), 021201 (Jan 13, 2009) (6 pages) doi:10.1115/1.3057403 History: Received October 31, 2007; Revised July 08, 2008; Published January 13, 2009

This paper applies the variational multiscale theory to develop an explicit a posteriori error estimator for quantities of interest and linear functionals of the solution. The method is an extension of a previous work on global and local error estimates for solutions computed with stabilized methods. The technique is based on approximating an exact representation of the error formulated as a function of the fine-scale Green function. Numerical examples for the multidimensional transport equation confirm that the method can provide good local error estimates of quantities of interest both in the diffusive and the advective limit.

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Copyright © 2009 by American Society of Mechanical Engineers
Topics: Errors
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Figures

Grahic Jump Location
Figure 1

Local efficiencies for two different meshes (10×10 and 100×100) for a diffusive problem (right) and an advective problem (left). Top graphs: error at the element centers. Bottom graphs: error at the mesh nodes.

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Figure 2

Advection dominated problem. Efficiency of the pointwise error at the mesh nodes. Meshes of 10×10 (left) and 100×100 (right).

Grahic Jump Location
Figure 3

Diffusion dominated problem. Efficiency of the pointwise error at the mesh nodes. Meshes of 10×10 (left) and 100×100 (right).

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