Error analysis of a finite element method for the space-fractional parabolic equation

Bangti Jin; Raytcho Lazarov; Joseph Pasciak; Zhi Zhou

doi:10.1137/13093933X

Error analysis of a finite element method for the space-fractional parabolic equation

Bangti Jin
, Raytcho Lazarov
, Joseph Pasciak
, Zhi Zhou

Research output: Journal article publication › Journal article › Academic research › peer-review

94 Citations (Scopus)

Abstract

We study a spatial semidiscrete scheme using the standard Galerkin finite element method with piecewise linear finite elements, as well as fully discrete schemes based on the backward Euler method and the Crank-Nicolson method. Error estimates in the L2(D)- and Hα/2(D)-norm are derived for the semidiscrete scheme and in the L2(D)-norm for the fully discrete schemes. These estimates cover both smooth and nonsmooth initial data and are expressed directly in terms of the smoothness of the initial data. Extensive numerical results are presented to illustrate the theoretical results.

Original language	English
Pages (from-to)	2272-2294
Number of pages	23
Journal	SIAM Journal on Numerical Analysis
Volume	52
Issue number	5
DOIs	https://doi.org/10.1137/13093933X
Publication status	Published - 1 Jan 2014
Externally published	Yes

Keywords

Error estimate
Finite element method
Fully discrete scheme
Semidiscrete scheme
Space fractional parabolic equation

ASJC Scopus subject areas

Numerical Analysis

More information

10.1137/13093933X

Cite this

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title = "Error analysis of a finite element method for the space-fractional parabolic equation",

abstract = "We study a spatial semidiscrete scheme using the standard Galerkin finite element method with piecewise linear finite elements, as well as fully discrete schemes based on the backward Euler method and the Crank-Nicolson method. Error estimates in the L2(D)- and Hα/2(D)-norm are derived for the semidiscrete scheme and in the L2(D)-norm for the fully discrete schemes. These estimates cover both smooth and nonsmooth initial data and are expressed directly in terms of the smoothness of the initial data. Extensive numerical results are presented to illustrate the theoretical results.",

keywords = "Error estimate, Finite element method, Fully discrete scheme, Semidiscrete scheme, Space fractional parabolic equation",

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T1 - Error analysis of a finite element method for the space-fractional parabolic equation

AU - Jin, Bangti

AU - Lazarov, Raytcho

AU - Pasciak, Joseph

AU - Zhou, Zhi

PY - 2014/1/1

Y1 - 2014/1/1

N2 - We study a spatial semidiscrete scheme using the standard Galerkin finite element method with piecewise linear finite elements, as well as fully discrete schemes based on the backward Euler method and the Crank-Nicolson method. Error estimates in the L2(D)- and Hα/2(D)-norm are derived for the semidiscrete scheme and in the L2(D)-norm for the fully discrete schemes. These estimates cover both smooth and nonsmooth initial data and are expressed directly in terms of the smoothness of the initial data. Extensive numerical results are presented to illustrate the theoretical results.

AB - We study a spatial semidiscrete scheme using the standard Galerkin finite element method with piecewise linear finite elements, as well as fully discrete schemes based on the backward Euler method and the Crank-Nicolson method. Error estimates in the L2(D)- and Hα/2(D)-norm are derived for the semidiscrete scheme and in the L2(D)-norm for the fully discrete schemes. These estimates cover both smooth and nonsmooth initial data and are expressed directly in terms of the smoothness of the initial data. Extensive numerical results are presented to illustrate the theoretical results.

KW - Error estimate

KW - Finite element method

KW - Fully discrete scheme

KW - Semidiscrete scheme

KW - Space fractional parabolic equation

UR - https://www.scopus.com/pages/publications/84911443704

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DO - 10.1137/13093933X

M3 - Journal article

SN - 0036-1429

VL - 52

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EP - 2294

JO - SIAM Journal on Numerical Analysis

JF - SIAM Journal on Numerical Analysis

IS - 5

ER -

Error analysis of a finite element method for the space-fractional parabolic equation

Abstract

Keywords

ASJC Scopus subject areas

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