A finite element method for the multiterm time-space Riesz fractional advection-diffusion equations in finite domain
type: Item
instance of: scholarly article
title: A finite element method for the multiterm time-space Riesz fractional advection-diffusion equations in finite domain
zbMATH Open document ID: 1275.65064
DOI: 10.1155/2013/868035
author: Jingjun Zhao
author: Jingyu Xiao
author: Yang Xu
published in: Abstract and Applied Analysis
publication date: 2013-09-19T00:00:00Z
review text: Summary: We present an effective finite element method (FEM) for the multiterm time-space Riesz fractional advection-diffusion equations (MT-TS-RFADEs). We obtain the weak formulation of MT-TS-RFADEs and prove the existence and uniqueness of weak solutions by the Lax-Milgram theorem. For multiterm time discretization, we use the Diethelm fractional backward finite difference method based on quadrature. For spatial discretization, we show the details of an FEM for such MT-TS-RFADEs. Then, stability and convergence of such numerical method are proved, and some numerical examples are given to match well with the main conclusions.
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 65M06
Mathematics Subject Classification ID: 65M12
Mathematics Subject Classification ID: 35R11
zbMATH DE Number: 6209480
zbMATH Keywords: finite element method
zbMATH Keywords: multiterm time-space Riesz fractional advection-diffusion equations
zbMATH Keywords: Diethelm fractional backward finite difference method
zbMATH Keywords: stability
zbMATH Keywords: convergence
zbMATH Keywords: numerical examples
Wikidata QID: Q58917643
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/868035
OpenAlex ID: W2006632746
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description: scientific article; zbMATH DE number 6209480