An hp-adaptive Newton-Galerkin finite element procedure for semilinear boundary value problems

被引：4

作者：

Amrein, Mario ^{[1
]}

Melenk, Jens Markus ^{[2
]}

Wihler, Thomas P. ^{[3
]}

机构：

[1] Lucerne Univ Appl Sci & Arts, CH-6002 Luzern, Switzerland

[2] TU Wien, Inst Anal & Sci Comp, A-1040 Vienna, Austria

[3] Univ Bern, Math Inst, CH-3012 Bern, Switzerland

来源：

MATHEMATICAL METHODS IN THE APPLIED SCIENCES | 2017年 / 40卷 / 06期

基金：

瑞士国家科学基金会;

关键词：

adaptive Newton methods; semilinear elliptic problems; singularly perturbed problems; adaptive finite element methods; hp-FEM; hp-adaptivity; PARTIAL-DIFFERENTIAL-EQUATIONS; ERROR ESTIMATORS; LINEARIZATION;

D O I：

10.1002/mma.4113

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we develop an hp-adaptive procedure for the numerical solution of general, semilinear elliptic boundary value problems in 1d, with possible singular perturbations. Our approach combines both a prediction-type adaptive Newton method and an hp-version adaptive finite element discretization (based on a robust a posteriori residual analysis), thereby leading to a fully hp-adaptive Newton-Galerkin scheme. Numerical experiments underline the robustness and reliability of the proposed approach for various examples. Copyright (c) 2016 John Wiley & Sons, Ltd.

引用

页码：1973 / 1985

页数：13

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