Premium
Analysis of DG approximations for Stokes problem based on velocity‐pseudostress formulation
Author(s) -
Barrios Tomás P.,
Bustinza Rommel,
Sánchez Felipe
Publication year - 2017
Publication title -
numerical methods for partial differential equations
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.901
H-Index - 61
eISSN - 1098-2426
pISSN - 0749-159X
DOI - 10.1002/num.22152
Subject(s) - mathematics , a priori and a posteriori , convergence (economics) , uniqueness , stokes problem , scheme (mathematics) , partial differential equation , rate of convergence , work (physics) , stokes flow , mathematical analysis , finite element method , key (lock) , computer science , geometry , mechanical engineering , philosophy , flow (mathematics) , physics , computer security , epistemology , engineering , economics , thermodynamics , economic growth
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