Fully Adaptive Newton-Galerkin Methods for Semilinear Elliptic Partial Differential Equations
For researchers solving semilinear elliptic PDEs, this provides a robust adaptive scheme, though it is an incremental combination of existing methods.
The paper develops a fully adaptive Newton-Galerkin method for semilinear elliptic PDEs, combining an adaptive Newton method with adaptive finite elements. Numerical experiments demonstrate robustness and reliability.
In this paper we develop an adaptive procedure for the numerical solution of general, semilinear elliptic problems with possible singular perturbations. Our approach combines both a prediction-type adaptive Newton method and an adaptive finite element discretization (based on a robust a posteriori error analysis), thereby leading to a fully adaptive Newton-Galerkin scheme. Numerical experiments underline the robustness and reliability of the proposed approach for different examples.