An hp-Adaptive Iterative Linearization Discontinuous-Galerkin FEM for Quasilinear Elliptic Boundary Value Problems

Abstract

In this article we consider the a posteriori error analysis of hp-version discontinuous Galerkin finite element methods for the numerical solution of a second-order quasilinear elliptic boundary value problem of strongly monotone type. In particular, we employ and analyze a practical solution scheme based on exploiting a discrete Kačanov iterative linearization. The resulting a posteriori error bound explicitly takes into account the three sources of error: discretization, linearization, and linear solver errors. Numerical experiments are presented to demonstrate the practical performance of the proposed hp-adaptive refinement strategy.