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In this paper, we develop an  h  p ‐adaptive procedure for the numerical solution of general, semilinear elliptic boundary value problems in 1d, with possible singular perturbations. Our approach combines both a prediction‐type adaptive Newton method and an  h  p ‐version adaptive finite element discretization (based on a robust  a posteriori  residual analysis), thereby leading to a fully  h  p ‐adaptive Newton–Galerkin scheme. Numerical experiments underline the robustness and reliability of the proposed approach for various examples. Copyright © 2016 John Wiley & Sons, Ltd.

An h p ‐adaptive Newton‐Galerkin finite element procedure for semilinear boundary value problems