@Article{IJNAM-11-496,
author = {S. Congreve and P. Houston},
title = {Two-Grid $hp$-Version Discontinuous Galerkin Finite Element Methods for Quasi-Newtonian Fluid Flows},
journal = {International Journal of Numerical Analysis and Modeling},
year = {2014},
volume = {11},
number = {3},
pages = {496--524},
abstract = {<p style="text-align: justify;">In this article we consider the a priori and a posteriori error analysis of two-grid $hp$-version discontinuous Galerkin finite element methods for the numerical solution of a strongly
monotone quasi-Newtonian fluid flow problem. The basis of the two-grid method is to first solve
the underlying nonlinear problem on a coarse finite element space; a fine grid solution is then
computed based on undertaking a suitable linearization of the discrete problem. Here, we study
two alternative linearization techniques: the first approach involves evaluating the nonlinear viscosity
coefficient using the coarse grid solution, while the second method utilizes an incomplete
Newton iteration technique. Energy norm error bounds are deduced for both approaches. Moreover,
we design an $hp$-adaptive refinement strategy in order to automatically design the underlying
coarse and fine finite element spaces. Numerical experiments are presented which demonstrate
the practical performance of both two-grid discontinuous Galerkin methods.</p>},
issn = {2617-8710},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/ijnam/539.html}
}