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Center for Computational and Applied Mathematics

Discontinuous Petrov Galerkin (DPG) Method with Optimal Test Functions

Leszek Demkowicz
The University of Texas at Austin
Website of Leszek Demkowicz

Location: Purdue University

Apr 26, 2014 9:30 AM

The DPG methodology allows for controlling the norm in which we want to converge by selecting an appropriate norm for residual. I will outline a general strategy for determining the optimal test norms in context of general singular perturbation problems focusing on convection-dominated diffusion [1,2], incompressible [3] and compressible [4] Navier-Stokes equations.

  1. L. Demkowicz and N. Heuer,``Robust DPG Method for Convection-Dominated Diffusion Problems'', SIAM J. Num. Anal 51: 2514-2537, 2013, see also ICES Report 2011/13.
  2. J. Chan, N, Heuer, T Bui-Thanh and L. Demkowicz, `` Robust DPG Method for Convection-dominated Diffusion Problems II: Natural Inflow Condition'', Comput. Math. Appl., 2013, in print, see also ICES Report 2012/21.
  3. Nathan Roberts. ``A Discontinuous Petrov-Galerkin Methodology for Incompressible Flow Problems'', PhD thesis, University of Texas at Austin, August 2013. (supervisors: L. Demkowicz and R. Moser).
  4. Jesse Chan,``A DPG Method for Convection-Diffusion Problems'', PhD thesis, University of Texas at Austin, July 2013 (supervisors: L. Demkowicz and R. Moser).