ROBUST DPG METHOD FOR CONVECTION-DOMINATED DIFFUSION PROBLEMS

We propose and analyze a discontinuous Petrov–Galerkin (DPG) method for convection-dominated diffusion problems that provides robust L2 error estimates for the field variables which are quasi-optimal in the energy norm. A key feature of the method is to construct test functions defined by a variatio...

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Bibliographic Details
Published in:SIAM journal on numerical analysis 2013-01, Vol.51 (5), p.2514-2537
Main Authors: DEMKOWICZ, LESZEK, HEUER, NORBERT
Format: Article
Language:English
Subjects:
Adjoints
Approximation
Construction specifications
Diffusion
Energy
Error analysis
Mathematical analysis
Mathematical models
Norms
Robustness
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Summary:We propose and analyze a discontinuous Petrov–Galerkin (DPG) method for convection-dominated diffusion problems that provides robust L2 error estimates for the field variables which are quasi-optimal in the energy norm. A key feature of the method is to construct test functions defined by a variational formulation with bilinear form (test norm) specifically designed for the goal of robustness. A main theoretical ingredient is a stability analysis of the adjoint problem. Numerical experiments underline our theoretical results and, in particular, confirm robustness of the DPG method for well-chosen test norms.
ISSN:0036-1429
1095-7170
DOI:10.1137/120862065