科研之友
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摘要
In this article, we develop an adaptive procedure for the numerical solution of semilinear parabolic problems with possible singular perturbations. Our approach combines a linearization technique using Newton's method with an adaptive discretization-which is based on a spatial finite element method and the backward Euler time-stepping scheme-of the resulting sequence of linear problems. Upon deriving a robust a posteriori error analysis, we design a fully adaptive Newton-Galerkin time-stepping algorithm. Numerical experiments underline the robustness and reliability of the proposed approach for various examples.
- 出版日期2017-10
