A Performance Comparison of Continuous and Discontinuous Finite Element Shallow Water Models
Journal of Scientific Computing
Error estimates for a finite element-finite volume discretization of convection-diffusion equations
Applied Numerical Mathematics
Analysis of an Interface Stabilized Finite Element Method: The Advection-Diffusion-Reaction Equation
SIAM Journal on Numerical Analysis
To CG or to HDG: A Comparative Study
Journal of Scientific Computing
Computers & Mathematics with Applications
Journal of Scientific Computing
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We study a multiscale discontinuous Galerkin method introduced in [T. J. R. Hughes, G. Scovazzi, P. Bochev, and A. Buffa, Comput. Meth. Appl. Mech. Engrg., 195 (2006), pp. 2761-2787] that reduces the computational complexity of the discontinuous Galerkin method, seemingly without adversely affecting the quality of results. For a stabilized variant we are able to obtain the same error estimates for the convection-diffusion equation as for the usual discontinuous Galerkin method. We assess the stability of the unstabilized case numerically and find that the inf-sup constant is positive, bounded uniformly away from zero, and very similar to that for the usual discontinuous Galerkin method.