Discontinuous Petrov-Galerkin method based on the optimal test space norm for one-dimensional transport problems | Zendy

Antti H. Niemi | Zendy; Nathaniel O. Collier | Zendy; Victor M. Calo | Zendy

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Discontinuous Petrov-Galerkin method based on the optimal test space norm for one-dimensional transport problems

Author(s) -

Antti H. Niemi,

Nathaniel O. Collier,

Victor M. Calo

Publication year - 2011

Publication title -

procedia computer science

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.334

H-Index - 76

ISSN - 1877-0509

DOI - 10.1016/j.procs.2011.04.202

Subject(s) - petrov–galerkin method , discretization , discontinuous galerkin method , computer science , finite element method , norm (philosophy) , mathematics , convection–diffusion equation , stability (learning theory) , function space , advection , mathematical optimization , mathematical analysis , physics , machine learning , political science , law , thermodynamics

We revisit the finite element analysis of convection dominated flow problems within the recently developed Discontinuous Petrov-Galerkin (DPG) variational framework. We demonstrate how test function spaces that guarantee numerical stability can be computed automatically with respect to the so called optimal test space norm by using an element subgrid discretization. This should make the DPG method not only stable but also robust, that is, uniformly stable with respect to the Ṕeclet number in the current application. The e_ectiveness of the algorithm is demonstrated on two problems for the linear advection-di_usion equation

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