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  4. Analysis of DG approximations for Stokes problem based on velocity-pseudostress formulation
 
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Analysis of DG approximations for Stokes problem based on velocity-pseudostress formulation
Dr. Barrios-Faúndez, Tomás 
Facultad de Ingeniería 
Bustinza, Rommel
Sánchez, Felipe
10.1002/num.22152
Numerical Methods for Partial Differential Equations
2017
In this article, we first discuss the well posedness of a modified LDG scheme of Stokes problem, considering a velocity-pseudostress formulation. The difficulty here relies on the fact that the application of classical Babuška-Brezzi theory is not easy, so we proceed in a nonstandard way. For uniqueness, we apply a discrete version of Fredholm's alternative theorem, while the a priori error analysis is done introducing suitable projections of exact solution. As a result, we prove that the method is convergent, and under suitable regularity assumptions on the exact solution, the optimal rate of convergence is guaranteed. Next, we explore two stabilizations to the previous scheme, by adding least squares type terms. For these cases, well posedness and the a priori error estimates are proved by the application of standard theory. We end this work with some numerical experiments considering our third scheme, whose results are in agreement with the theoretical properties we deduce.
Augmented formulation
Discontinuous Galerkin
Stokes problem
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