Robust exponential convergence of hp-FEM in balanced norms for singularly perturbed reaction-diffusion problems: Corner domains

被引：5

作者：

Faustmann, M. ^{[1
]}

Melenk, J. M. ^{[1
]}

机构：

[1] Tech Univ Wien, Wiedner Hauptstr 8-10, A-1040 Vienna, Austria

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 2017年 / 74卷 / 07期

关键词：

High order FEM; Singular perturbation; Balanced norm; Uniform estimates; FINITE-ELEMENT-METHOD; BOUNDARY-LAYERS;

D O I：

10.1016/j.camwa.2017.03.015

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The hp-version of the finite element method is applied to singularly perturbed reaction diffusion type equations on polygonal domains. The solution exhibits boundary layers as well as corner layers. On a class of meshes that are suitably refined near the boundary and the corners, robust exponential convergence (in the polynomial degree) is shown in both a balanced norm and the maximum norm. (C) 2017 Elsevier Ltd. All rights reserved.

引用

页码：1576 / 1589

页数：14

共 50 条

[41] Error Estimate in the Balanced Norm for the Singularly Perturbed Reaction–Diffusion Problems
Mishra P.
Babu G.
Sharma K.K.
[J]. International Journal of Applied and Computational Mathematics, 2023, 9 (5)
[42] Convergence and superconvergence analysis of an anisotropic nonconforming finite element methods for singularly perturbed reaction-diffusion problems
Zhu, Guoqing
Chen, Shaochun
[J]. JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2010, 234 (10) : 3048 - 3063
[43] Convergence and stability in balanced norms of finite element methods on Shishkin meshes for reaction-diffusion problems
Roos, Hans-Goerg
Schopf, Martin
[J]. ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, 2015, 95 (06): : 551 - 565
[44] Robust error estimation in energy and balanced norms for singularly perturbed fourth order problems
Franz, Sebastian
Roos, Hans-Goerg
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2016, 72 (01) : 233 - 247
[45] Mesh refinement strategies for solving singularly perturbed reaction-diffusion problems
Castaings, W
Navon, IM
[J]. COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2001, 41 (1-2) : 157 - 176
[46] A fitted numerical method for singularly perturbed parabolic reaction-diffusion problems
Munyakazi, Justin B.
Patidar, Kailash C.
[J]. COMPUTATIONAL & APPLIED MATHEMATICS, 2013, 32 (03): : 509 - 519
[47] A fitted numerical method for singularly perturbed parabolic reaction-diffusion problems
Justin B. Munyakazi
Kailash C. Patidar
[J]. Computational and Applied Mathematics, 2013, 32 : 509 - 519
[48] Difference scheme for singularly perturbed reaction-diffusion problems with concentrated capacity
Braianov, IA
Vulkov, LG
[J]. FINITE DIFFERENCE METHODS: THEORY AND APPLICATIONS, 1999, : 23 - 31
[49] Singularly perturbed reaction-diffusion problems on a k-star graph
Kumar, Vivek
Leugering, Guenter
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2021, 44 (18) : 14874 - 14891
[50] A mixed hp FEM for the approximation of fourth-order singularly perturbed problems on smooth domains
Constantinou, P.
Franz, S.
Ludwig, L.
Xenophontos, C.
[J]. NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2019, 35 (01) : 114 - 127

← 1 2 3 4 5 →