The Influence of the Stabilization term on DG and Hybrid DG formulations for Poisson Flow

Ismael S. Ledoino¹; Abimael F.D. Loula¹

¹ LNCC

doi:10.20906/CPS/CILAMCE2017-1098

Resumo

Discontinuous Galerkin (DG) methods have been applied to solve many problems in physics due to their well suited formulation for $p$-adaptivity techniques, as well their good accuracy for natural discontinuous problems. The disadvantage of more degrees of freedom when compared to continuous Galerkin methods has been removed with hibridization, simmetric formulations were introduced to ease linear system solving and stabilized formulations have been created to achieve coercivity of the bilinear form involved. The stabilization seems necessary, at least in the general setting, for the coercivity of the bilinear form. In 1974 \cite{BEVILACQUA19741091} created one of the first DG symmetric formulations for the non-homogeneous Poisson problem using an additional functional added to the original one. Their formulation was showed to work via numerical experiments, even though no stabilization term was added. In this work we seek for answers to why their formulation worked and what is the influence of the stabilization term to the numerical methods. We conduce numerical experiments confronting the results of DG and hybrid DG methods with no stabilization terms to the classical results expected for the non-homogeneous Poisson problem. @article{BEVILACQUA19741091, title = "A variational principle for the laplace's operator with application in the torsion of composite rods", journal = "International Journal of Solids and Structures", volume = "10", number = "10", pages = "1091 - 1102", year = "1974", note = "", issn = "0020-7683", doi = "http://dx.doi.org/10.1016/0020-7683(74)90060-2", url = "http://www.sciencedirect.com/science/article/pii/0020768374900602", author = "Luiz Bevilacqua and Raul Feijoo and Luis F.Rojas M", }

Palavras-chave: Finite Elements; Discontinous Galerkin; Stabilization