This work was partially supported by the NSF under grant DMS-1211635 and by the AFOSR under grant FA9550-12-1-0484.
Computers & Mathematics with Applications
Reformulation (Mathematical programming), Poisson’s equation, Mathematics -- Formulae, Approximation theory
We show that it is possible to apply the DPG methodology without reformulating a second-order boundary value problem into a first-order system, by considering the simple example of the Poisson equation. The result is a new weak formulation and a new DPG method for the Poisson equation, which has no numerical trace variable, but has a numerical flux approximation on the element interfaces, in addition to the primal interior variable.
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Demkowicz, L. L., & Gopalakrishnan, J. J. (2013). A primal DPG method without a first-order reformulation. Computers & Mathematics With Applications, 66(6), 1058-1064.