On the choice of stabilizing sub-grid for convection-diffusion problem on rectangular grids

Authors:
A. I. Nesliturk
Affiliations:
Izmir Institute of Technology, Department of Mathematics, 35430, Izmir, Turkey
Venue:
Computers & Mathematics with Applications
Year:
2010

Citing 4
Cited 2

Stabilized finite element methods. I: Application to the advective-diffusive model

Computer Methods in Applied Mechanics and Engineering
A Priori Error Analysis of Residual-Free Bubbles for Advection-Diffusion Problems

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Convergence Analysis of the Residual Free Bubble Method for Bilinear Elements

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Global and Local Error Analysis for the Residual-Free Bubbles Method Applied to Advection-Dominated Problems

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Applications of the pseudo residual-free bubbles to the stabilization of convection-diffusion-reaction problems

Calcolo: a quarterly on numerical analysis and theory of computation
Bubble and multiscale stabilization of bilinear finite element methods for transient advection-diffusion equations on rectangular grids

Journal of Computational and Applied Mathematics

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Abstract

A stabilizing sub-grid which consists of a single additional node in each rectangular element is analyzed for solving the convection-diffusion problem, especially in the case of small diffusion. We provide a simple recipe for spotting the location of the additional node that contributes a very good stabilizing effect to the overall numerical method. We further study convergence properties of the method under consideration and prove that the standard Galerkin finite element solution on augmented grid produces a discrete solution that satisfies the same type of a priori error estimates that are typically obtained with the SUPG method. Some numerical experiments that confirm the theoretical findings are also presented.