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SIAMSC
2008

The Compact Discontinuous Galerkin (CDG) Method for Elliptic Problems

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The Compact Discontinuous Galerkin (CDG) Method for Elliptic Problems
We present a compact discontinuous Galerkin (CDG) method for an elliptic model problem. The problem is first cast as a system of first order equations by introducing the gradient of the primal unknown, or flux, as an additional variable. A standard discontinuous Galerkin (DG) method is then applied to the resulting system of equations. The numerical inter-element fluxes are such that the equations for the additional variable can be eliminated at the element level, thus resulting in a global system that only involves the original unknown variable. The proposed method is closely related to the Local Discontinuous Galerkin (LDG) method [10], but, unlike the LDG method, the sparsity pattern of the CDG method only involves nearest neighbors. Also, unlike the LDG method, the CDG method works without stabilization for an arbitrary orientation of the element interfaces. The computation of the numerical interface fluxes for the CDG method is slightly more involved than for the LDG method, but t...
Jaime Peraire, Per-Olof Persson
Added 14 Dec 2010
Updated 14 Dec 2010
Type Journal
Year 2008
Where SIAMSC
Authors Jaime Peraire, Per-Olof Persson
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