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Spatial High Accuracy Analysis of FEM for Two-dimensional Multi-term Time-fractional Diffusion-wave Equations

Spatial High Accuracy Analysis of FEM for Two-dimensional Multi-term Time-fractional... In this paper, high-order numerical analysis of finite element method (FEM) is presented for two-dimensional multi-term time-fractional diffusion-wave equation (TFDWE). First of all, a fully-discrete approximate scheme for multi-term TFDWE is established, which is based on bilinear FEM in spatial direction and Crank-Nicolson approximation in temporal direction, respectively. Then the proposed scheme is proved to be unconditionally stable and convergent. And then, rigorous proofs are given here for superclose properties in H 1−norm and temporal convergence in L 2-norm with order $$O(h^{2}+\tau^{3-\alpha})$$ O ( h 2 + τ 3 − α ) , where h and τ are the spatial size and time step, respectively. At the same time, theoretical analysis of global superconvergence in H 1-norm is derived by interpolation postprocessing technique. At last, numerical example is provided to demonstrate the theoretical analysis. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Spatial High Accuracy Analysis of FEM for Two-dimensional Multi-term Time-fractional Diffusion-wave Equations

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References (59)

Publisher
Springer Journals
Copyright
Copyright © 2018 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag GmbH Germany, part of Springer Nature
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-018-0795-1
Publisher site
See Article on Publisher Site

Abstract

In this paper, high-order numerical analysis of finite element method (FEM) is presented for two-dimensional multi-term time-fractional diffusion-wave equation (TFDWE). First of all, a fully-discrete approximate scheme for multi-term TFDWE is established, which is based on bilinear FEM in spatial direction and Crank-Nicolson approximation in temporal direction, respectively. Then the proposed scheme is proved to be unconditionally stable and convergent. And then, rigorous proofs are given here for superclose properties in H 1−norm and temporal convergence in L 2-norm with order $$O(h^{2}+\tau^{3-\alpha})$$ O ( h 2 + τ 3 − α ) , where h and τ are the spatial size and time step, respectively. At the same time, theoretical analysis of global superconvergence in H 1-norm is derived by interpolation postprocessing technique. At last, numerical example is provided to demonstrate the theoretical analysis.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Oct 4, 2018

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