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

作者：Congreve Scott; Houston Paul^*; Sueli Endre; Wihler Thomas P

来源：IMA Journal of Numerical Analysis, 2013, 33(4): 1386-1415.

DOI：10.1093/imanum/drs046

• hp-version finite element methods
• discontinuous Galerkin methods
• hp-adaptivity
• quasilinear PDEs
• quasi-Newtonian flows

In this article, we develop 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 of 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.

• 出版日期2013-10