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

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

5 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)

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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.",

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author = "Masahisa Tabata and Shinya Uchiumi",

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AU - Tabata, Masahisa

AU - Uchiumi, Shinya

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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

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