An hp-adaptive iterative linearization discontinuous-Galerkin FEM for quasilinear elliptic boundary value problems

Houston, Paul; Wihler, Thomas P (2020). An hp-adaptive iterative linearization discontinuous-Galerkin FEM for quasilinear elliptic boundary value problems. In: Sherwin, Spencer J; Moxey, David; Peiró, Joaquim; Vincent, Peter E; Schwab, Christoph (eds.) Spectral and high order methods for partial differential equations. ICOSAHOM 2018. Lecture Notes in Computational Science and Engineering: Vol. 134 (pp. 407-417). Springer 10.1007/978-3-030-39647-3_32

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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.

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