Contributions to Books:
M. Amrein, J. Melenk, T. Wihler:
"An hp-adaptive Newton-Galerkin finite element procedure for semilinear boundary value problems";
in: "ASC Report 6/2016",
issued by: Institute for Analysis and Scientific Computing;
Vienna University of Technology,
In this paper we develop an hp-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 hp-version adaptive ﬁnite element discretization (based on a robust a posteriori residual analysis), thereby leading to a fully hp-adaptive Newton-Galerkin scheme. Numerical experiments underline the robustness and reliability of the proposed approach for various examples.
Adaptive Newton methods, semilinear elliptic problems, singularly perturbed problems, adaptive ﬁnite element methods, hp-FEM, hp-adaptivity problems
Electronic version of the publication:
Created from the Publication Database of the Vienna University of Technology.