Local discontinuous Galerkin method with reduced stabilization for diffusion equations

Erik Burman (1) , Benjamin Stamm (2)

1 department of mathematics
2 LJLL - Laboratoire Jacques-Louis Lions

We extend the results on minimal stabilization of Burman and Stamm [J. Sci. Comp., 33 (2007), pp.~183-208] to the case of the local discontinuous Galerkin methods on mixed form. The penalization term on the faces is relaxed to act only on a part of the polynomial spectrum. Stability in the form of a discrete inf-sup condition is proved and optimal convergence follows. Some numerical examples using high order approximation spaces illustrate the theory.

Mots clés: Local discontinuous Galerkin h-FEM; interior penalty; diffusion equation

Domaines: Analyse numérique [math.NA]

Erik Burman, Benjamin Stamm. Local discontinuous Galerkin method with reduced stabilization for diffusion equations. Communications in Computational Physics, 2008, 5, pp.498-514. ⟨hal-01090926⟩