Analysis of DG approximations for Stokes problem based on velocity‐pseudostress formulation. Issue 5 (31st March 2017)

• Record Type: Journal Article
• Authors: Barrios, Tomás P.; Bustinza, Rommel; Sánchez, Felipe
• Is Part Of: Numerical methods for partial differential equations. Volume 33:Issue 5(2017:Sep.)
• Page Start: 1540
• Page End: 1564
• Publication Date: 2017-03-31
• Subjects: augmented formulation -- discontinuous Galerkin -- Stokes problem; Differential equations, Partial -- Numerical solutions -- Periodicals; 515.353
• DOI: 10.1002/num.22152
• Languages: English
• ISSNs: 0749-159X

Abstract

Abstract : 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.© 2017 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 33: 1540–1564, 2017