Journal
MATHEMATICS OF COMPUTATION
Volume 87, Issue 314, Pages 2641-2674Publisher
AMER MATHEMATICAL SOC
DOI: 10.1090/mcom/3308
Keywords
Newton method; semilinear elliptic problems; adaptive finite element methods; discontinuous Galerkin methods; hp-adaptivity
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Funding
- Swiss National Science Foundation (SNF) [200021-162990]
- Swiss National Science Foundation (SNF) [200021_162990] Funding Source: Swiss National Science Foundation (SNF)
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In this paper we develop an hp-adaptive procedure for the numerical solution of general second-order semilinear elliptic boundary value problems, with possible singular perturbation. Our approach combines both adaptive Newton schemes and an hp-version adaptive discontinuous Galerkin finite element discretisation, which, in turn, is based on a robust hp-version a posteriori residual analysis. Numerical experiments underline the robustness and reliability of the proposed approach for various examples.
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