An ℎ𝑝-adaptive Newton-discontinuous-Galerkin finite element approach for semilinear elliptic boundary value problems

Houston, Paul; Wihler, Thomas

doi:10.1090/mcom/3308

An $hp$-adaptive Newton-discontinuous-Galerkin finite element approach for semilinear elliptic boundary value problems
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Math. Comp. 87 (2018), 2641-2674 Request permission

Abstract:

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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