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

[21] Fully computable robust a posteriori error bounds for singularly perturbed reaction-diffusion problems
Ainsworth, Mark
Vejchodsky, Tomas
[J]. NUMERISCHE MATHEMATIK, 2011, 119 (02) : 219 - 243
[22] A Finite Element Method for Singularly Perturbed Reaction-diffusion Problems
Da-Li Zhang
[J]. Acta Mathematicae Applicatae Sinica, 2003, (01) : 25 - 30
[23] Nitsche Type Mortaring for Singularly Perturbed Reaction-diffusion Problems
B. Heinrich
K. Pönitz
[J]. Computing, 2005, 75 : 257 - 279
[24] A New Numerical Scheme for Singularly Perturbed Reaction-Diffusion Problems
Temel, Zelal
Cakir, Musa
[J]. GAZI UNIVERSITY JOURNAL OF SCIENCE, 2023, 36 (02): : 792 - 805
[25] Nitsche type mortaring for singularly perturbed reaction-diffusion problems
Heinrich, B
Pönitz, K
[J]. COMPUTING, 2005, 75 (04) : 257 - 279
[26] EXPONENTIAL CONVERGENCE OF A GENERALIZED FEM FOR HETEROGENEOUS REACTION-DIFFUSION EQUATIONS
Ma, Chupeng
Melenk, J. M.
[J]. MULTISCALE MODELING & SIMULATION, 2024, 22 (01): : 256 - 282
[27] Singularly Perturbed Reaction-Diffusion Problems as First order systems
Franz, Sebastian
[J]. JOURNAL OF SCIENTIFIC COMPUTING, 2021, 89 (02)
[28] On the uniform convergence of a finite difference scheme for time dependent singularly perturbed reaction-diffusion problems
Clavero, C.
Gracia, J. L.
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2010, 216 (05) : 1478 - 1488
[29] A Finite Element Method for Singularly Perturbed Reaction-diffusion Problems
Huo-yuan Duan
Da-Li Zhang
[J]. Acta Mathematicae Applicatae Sinica, 2003, 19 (1) : 25 - 30
[30] Numerical Solutions of a System of Singularly Perturbed Reaction-Diffusion Problems
Barati, Ali
Atabaigi, Ali
[J]. FILOMAT, 2019, 33 (15) : 4889 - 4905

← 1 2 3 4 5 →