Fully adaptive Newton--Galerkin methods for semilinear elliptic partial differential equations
M Amrein, TP Wihler - SIAM Journal on Scientific Computing, 2015 - SIAM
M Amrein, TP Wihler
SIAM Journal on Scientific Computing, 2015•SIAMIn this paper we develop an adaptive procedure for the numerical solution of general,
semilinear elliptic problems with possible singular perturbations. Our approach combines
both prediction-type adaptive Newton methods and a linear 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 various examples.
semilinear elliptic problems with possible singular perturbations. Our approach combines
both prediction-type adaptive Newton methods and a linear 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 various examples.
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 prediction-type adaptive Newton methods and a linear 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 various examples.
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