A comparison of discontinuous and continuous Galerkin methods based on error estimates, conservation, robustness and efficiency. (English) Zbl 0946.65109

Hughes, Thomas J. R.; Engel, Gerald; Mazzei, Luca; Larson, Mats G.

Cockburn, Bernardo (ed.) et al., Discontinuous Galerkin methods. Theory, computation and applications. 1st international symposium on DGM, Newport, RI, USA, May 24-26, 1999. Berlin: Springer. Lect. Notes Comput. Sci. Eng. 11, 135-146 (2000).

Summary: The discontinuous Galerkin method (DGM) and the continuous Galerkin method (CGM) are investigated and compared for the advection problem and the diffusion problem. First, error estimates for stabilized discontinuous Galerkin methods (SDGMs) are presented. Then, conservation laws are discussed for the DGM and CGM. An advantage ascribed to the DGM is the local flux conservation property. It is remarked that the CGM is not only globally conservative, but locally conservative too when a simple post-processing procedure is used. Next, the robustness of different DGMs is investigated numerically. Lastly, the efficiency of the DGM and CGM is compared.
For the entire collection see [Zbl 0935.00043].

MSC:

65N30	Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25	Boundary value problems for second-order elliptic equations
35L45	Initial value problems for first-order hyperbolic systems
65M60	Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
65N15	Error bounds for boundary value problems involving PDEs
65M15	Error bounds for initial value and initial-boundary value problems involving PDEs

Keywords:

error estimates; advection problem; diffusion problem; stabilized discontinuous Galerkin methods; conservation laws