SUPG and Residual-Free Bubbles are closely related methods that have been used with success to stabilize a certain number of problems, including advection dominated flows. In recent times, a slightly different idea has been proposed: to choose a suitable subgrid in each element, and then solving Standard Galerkin on the Augmented Grid. For this, however, the correct location of the subgrid node(s) plays a crucial role. Here, for the model problem of linear advection-diffusion equations, we propose a simple criterion to choose a single internal node such that the corresponding plain-Galerkin scheme on the augmented grid provides the same a priori error estimates that are typically obtained with SUPG or RFB methods.
Russo, A., Brezzi, F., Marini, L. (2005). On the choice of a stabilizing subgrid for convection-diffusion problems. COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 194(2-5), 127-148 [10.1016/j.cma.2004.02.022].
On the choice of a stabilizing subgrid for convection-diffusion problems
RUSSO, ALESSANDRO;
2005
Abstract
SUPG and Residual-Free Bubbles are closely related methods that have been used with success to stabilize a certain number of problems, including advection dominated flows. In recent times, a slightly different idea has been proposed: to choose a suitable subgrid in each element, and then solving Standard Galerkin on the Augmented Grid. For this, however, the correct location of the subgrid node(s) plays a crucial role. Here, for the model problem of linear advection-diffusion equations, we propose a simple criterion to choose a single internal node such that the corresponding plain-Galerkin scheme on the augmented grid provides the same a priori error estimates that are typically obtained with SUPG or RFB methods.
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