An hp-adaptive Newton-discontinuous-Galerkin finite element approach for semilinear elliptic boundary value problems - Houston, Paul; Wihler, Thomas P. (American Mathematical Society, 2018)
In this paper we develop an hp-adaptive procedure for the numerical solution of general second-order semilinear elliptic boundary value problems, with possible singular perturbation. Our approach combines both adaptive Newton schemes and an hp-version adaptive discontinuous Galerkin finite element discretisation, which, in turn, is based on a robust hp-version a posteriori residual analysis. Numerical experiments underline the robustness and reliability of the proposed approach for various examples.