Discontinuous Galerkin finite element approximation of quasilinear elliptic boundary value problems II: Strongly monotone quasi-Newtonian flows

Report

In this article we develop both the a priori and a posteriori error analysis of hp–version interior penalty discontinuous Galerkin finite element methods for strongly monotone quasi-Newtonian fluid flows in a bounded Lipschitz domain $ \Omega \subset R^{d}, d$ = 2,3. In the latter case, computable upper and lower bounds on the error are derived in terms of a natural energy norm which are explicit in the local mesh size and local polynomial degree of the approximating finite element method. A series of numerical experiments illustrate the performance of the proposed a posteriori error indicators within an automatic hp–adaptive refinement algorithm.

Authors: Congreve, S; Houston, P; Suli, E; Wihler, T

• Publisher: IMA Journal of Numerical Analysis
• Publication date: 2011-12-01