Finite element solutions for the space fractional diffusion equation with a nonlinear source term
type: Item
instance of: scholarly article
title: Finite element solutions for the space fractional diffusion equation with a nonlinear source term
zbMATH Open document ID: 1253.65148
DOI: 10.1155/2012/596184
author: Yanyan Li
published in: Abstract and Applied Analysis
publication date: 2012-12-18T00:00:00Z
review text: Summary: We consider finite element Galerkin solutions for the space fractional diffusion equation with a nonlinear source term. Existence, stability, and order of convergence of approximate solutions for the backward Euler fully discrete scheme have been discussed as well as for the semidiscrete scheme. The analytical convergent orders are obtained as \(O(k + h^{\tilde{\gamma}})\), where \(\tilde{\gamma}\) is a constant depending on the order of fractional derivative. Numerical computations are presented, which confirm the theoretical results when the equation has a linear source term. When the equation has a nonlinear source term, numerical results show that the diffusivity depends on the order of fractional derivative as we expect.
Mathematics Subject Classification ID: 65M60
Mathematics Subject Classification ID: 35R11
Mathematics Subject Classification ID: 35K57
zbMATH DE Number: 6116421
zbMATH Keywords: finite element Galerkin solutions
zbMATH Keywords: space fractional diffusion equation
Wikidata QID: Q58695644
describes a project that uses: FODE
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/596184
OpenAlex ID: W2136655753
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description: scientific article; zbMATH DE number 6116421