Maximum-norm a posteriori error estimates for singularly perturbed reaction-diffusion problems on anisotropic meshes

Natalia Kopteva

doi:10.1137/140983458

Maximum-norm a posteriori error estimates for singularly perturbed reaction-diffusion problems on anisotropic meshes

Natalia Kopteva

Research output: Contribution to journal › Article › peer-review

Abstract

Residual-type a posteriori error estimates in the maximum norm are given for singularly perturbed semilinear reaction-diffusion equations posed in polygonal domains. Linear finite elements are considered on anisotropic triangulations. The error constants are independent of the diameters and the aspect ratios of mesh elements and of the small perturbation parameter.

Original language	English
Pages (from-to)	2519-2544
Number of pages	26
Journal	SIAM Journal on Numerical Analysis
Volume	53
Issue number	6
DOIs	https://doi.org/10.1137/140983458
Publication status	Published - 2015

Keywords

A posteriori error estimate
Anisotropic triangulation
Maximum norm
Reaction-diffusion
Singular perturbation

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10.1137/140983458

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title = "Maximum-norm a posteriori error estimates for singularly perturbed reaction-diffusion problems on anisotropic meshes",

abstract = "Residual-type a posteriori error estimates in the maximum norm are given for singularly perturbed semilinear reaction-diffusion equations posed in polygonal domains. Linear finite elements are considered on anisotropic triangulations. The error constants are independent of the diameters and the aspect ratios of mesh elements and of the small perturbation parameter.",

keywords = "A posteriori error estimate, Anisotropic triangulation, Maximum norm, Reaction-diffusion, Singular perturbation",

author = "Natalia Kopteva",

note = "Publisher Copyright: {\textcopyright} 2015 Society for Industrial and Applied Mathematics.",

year = "2015",

doi = "10.1137/140983458",

language = "English",

volume = "53",

pages = "2519--2544",

journal = "SIAM Journal on Numerical Analysis",

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number = "6",

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T1 - Maximum-norm a posteriori error estimates for singularly perturbed reaction-diffusion problems on anisotropic meshes

AU - Kopteva, Natalia

PY - 2015

Y1 - 2015

N2 - Residual-type a posteriori error estimates in the maximum norm are given for singularly perturbed semilinear reaction-diffusion equations posed in polygonal domains. Linear finite elements are considered on anisotropic triangulations. The error constants are independent of the diameters and the aspect ratios of mesh elements and of the small perturbation parameter.

AB - Residual-type a posteriori error estimates in the maximum norm are given for singularly perturbed semilinear reaction-diffusion equations posed in polygonal domains. Linear finite elements are considered on anisotropic triangulations. The error constants are independent of the diameters and the aspect ratios of mesh elements and of the small perturbation parameter.

KW - A posteriori error estimate

KW - Anisotropic triangulation

KW - Maximum norm

KW - Reaction-diffusion

KW - Singular perturbation

UR - https://www.scopus.com/pages/publications/84973390112

U2 - 10.1137/140983458

DO - 10.1137/140983458

M3 - Article

AN - SCOPUS:84973390112

SN - 0036-1429

VL - 53

SP - 2519

EP - 2544

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

IS - 6

ER -

Maximum-norm a posteriori error estimates for singularly perturbed reaction-diffusion problems on anisotropic meshes

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Keywords

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