Two-Grid hp-Version DGFEMs for Strongly Monotone Second-Order Quasilinear Elliptic PDEs

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Abstract

In this article we develop the a priori error analysis of so-called two-grid hp-version discontinuous Galerkin finite element methods for the numerical approximation of strongly monotone second-order quasilinear partial differential equations. In this setting, the fully nonlinear problem is first approximated on a coarse finite element space V(��H,P). The resulting ‘coarse’ numerical solution is then exploited to provide the necessary data needed to linearize the underlying discretization on the finer space V(��h,p); thereby, only a linear system of equations is solved on the richer space V(��h,p). Numerical experiments confirming the theoretical results are presented. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)

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