A genuinely stable Lagrange–Galerkin scheme for convection-diffusion problems

Masahisa Tabata; Shinya Uchiumi

doi:10.1007/s13160-015-0196-2

A genuinely stable Lagrange–Galerkin scheme for convection-diffusion problems

Masahisa Tabata^*, Shinya Uchiumi

^*Corresponding author for this work

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

8 Citations (Scopus)

Abstract

We present a Lagrange–Galerkin scheme free from numerical quadrature for convection-diffusion problems. Since the scheme can be implemented exactly as it is, theoretical stability result is assured. While conventional Lagrange–Galerkin schemes may encounter the instability caused by numerical quadrature error, the present scheme is genuinely stable. For the (Formula presented.) -element we prove error estimates of (Formula presented.) in (Formula presented.) -norm and of (Formula presented.) in (Formula presented.) -norm. Numerical results reflect these estimates.

Original language	English
Pages (from-to)	121-143
Number of pages	23
Journal	Japan Journal of Industrial and Applied Mathematics
Volume	33
Issue number	1
DOIs	https://doi.org/10.1007/s13160-015-0196-2
Publication status	Published - 2016 Feb 1

Keywords

Convection-diffusion problems
Exact integration
Finite element method
Lagrange–Galerkin scheme

ASJC Scopus subject areas

Applied Mathematics
Engineering(all)

Access to Document

10.1007/s13160-015-0196-2

Cite this

@article{65711ca409794b74825e35cca1b5e7ff,

title = "A genuinely stable Lagrange–Galerkin scheme for convection-diffusion problems",

abstract = "We present a Lagrange–Galerkin scheme free from numerical quadrature for convection-diffusion problems. Since the scheme can be implemented exactly as it is, theoretical stability result is assured. While conventional Lagrange–Galerkin schemes may encounter the instability caused by numerical quadrature error, the present scheme is genuinely stable. For the (Formula presented.) -element we prove error estimates of (Formula presented.) in (Formula presented.) -norm and of (Formula presented.) in (Formula presented.) -norm. Numerical results reflect these estimates.",

keywords = "Convection-diffusion problems, Exact integration, Finite element method, Lagrange–Galerkin scheme",

author = "Masahisa Tabata and Shinya Uchiumi",

year = "2016",

month = feb,

day = "1",

doi = "10.1007/s13160-015-0196-2",

language = "English",

volume = "33",

pages = "121--143",

journal = "Japan Journal of Industrial and Applied Mathematics",

issn = "0916-7005",

publisher = "Springer Japan",

number = "1",

}

TY - JOUR

T1 - A genuinely stable Lagrange–Galerkin scheme for convection-diffusion problems

AU - Tabata, Masahisa

AU - Uchiumi, Shinya

PY - 2016/2/1

Y1 - 2016/2/1

N2 - We present a Lagrange–Galerkin scheme free from numerical quadrature for convection-diffusion problems. Since the scheme can be implemented exactly as it is, theoretical stability result is assured. While conventional Lagrange–Galerkin schemes may encounter the instability caused by numerical quadrature error, the present scheme is genuinely stable. For the (Formula presented.) -element we prove error estimates of (Formula presented.) in (Formula presented.) -norm and of (Formula presented.) in (Formula presented.) -norm. Numerical results reflect these estimates.

AB - We present a Lagrange–Galerkin scheme free from numerical quadrature for convection-diffusion problems. Since the scheme can be implemented exactly as it is, theoretical stability result is assured. While conventional Lagrange–Galerkin schemes may encounter the instability caused by numerical quadrature error, the present scheme is genuinely stable. For the (Formula presented.) -element we prove error estimates of (Formula presented.) in (Formula presented.) -norm and of (Formula presented.) in (Formula presented.) -norm. Numerical results reflect these estimates.

KW - Convection-diffusion problems

KW - Exact integration

KW - Finite element method

KW - Lagrange–Galerkin scheme

UR - http://www.scopus.com/inward/record.url?scp=84958035944&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84958035944&partnerID=8YFLogxK

U2 - 10.1007/s13160-015-0196-2

DO - 10.1007/s13160-015-0196-2

M3 - Article

AN - SCOPUS:84958035944

VL - 33

SP - 121

EP - 143

JO - Japan Journal of Industrial and Applied Mathematics

JF - Japan Journal of Industrial and Applied Mathematics

SN - 0916-7005

IS - 1

ER -

A genuinely stable Lagrange–Galerkin scheme for convection-diffusion problems

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this