Sie befinden Sich nicht im Netzwerk der Universität Paderborn. Der Zugriff auf elektronische Ressourcen ist gegebenenfalls nur via VPN oder Shibboleth (DFN-AAI) möglich. mehr Informationen...
Finite difference/finite element method for a nonlinear time-fractional fourth-order reaction–diffusion problem
Ist Teil von
Computers & mathematics with applications (1987), 2015-08, Vol.70 (4), p.573-591
Ort / Verlag
Elsevier Ltd
Erscheinungsjahr
2015
Quelle
Access via ScienceDirect (Elsevier)
Beschreibungen/Notizen
In this article, a finite difference/finite element algorithm, which is based on a finite difference approximation in time direction and finite element method in spatial direction, is presented and discussed to cast about for the numerical solutions of a time-fractional fourth-order reaction–diffusion problem with a nonlinear reaction term. To avoid the use of higher-order elements, the original problem with spatial fourth-order derivative need to be changed into a second-order coupled system by introducing an intermediate variable σ=Δu. Then the fully discrete finite element scheme is formulated by using a finite difference approximation for time fractional and integer derivatives and finite element method in spatial direction. The unconditionally stable result in the norm, which just depends on initial value and source item, is derived. Some a priori estimates of L2-norm with optimal order of convergence O(Δt2−α+hm+1), where Δt and h are time step length and space mesh parameter, respectively, are obtained. To confirm the theoretical analysis, some numerical results are provided by our method.