High-order finite element methods for time-fractional partial differential equations

By Yingjun Jiang, Jingtang Ma. Journal of Computational and Applied Mathematics, 2011

414 citations recorded by the source corpus.

The aim of this paper is to develop high-order methods for solving time-fractional partial differential equations. The proposed high-order method is based on high-order finite element method for space and finite difference method for time. Optimal convergence rate O((@Dt)^2^-^@a+N^-^r) is proved for the (r-1)th-order finite element method (r>=2).

Subfields: Modeling and Simulation, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/bbd8d404388af47a4245a82e8b350df102e61f26

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Modeling and Simulation

1. Changpin Li
2. Fawang Liu
3. Ian L Turner
4. Fanhai Zeng
5. Yubin Yan
6. Neville J. Ford
7. Weihua Deng
8. Jingyu Xiao

In Numerical Analysis

1. Changpin Li
2. Fawang Liu
3. Ian L Turner
4. Fanhai Zeng
5. Yubin Yan
6. Neville J. Ford
7. Jingyu Xiao
8. Ting Wei

Citations in the corpus

• The Use of Finite Difference/Element Approaches for Solving the Time-Fractional Subdiffusion Equation (2013, methodology): “Comparisons are made between the derived algorithms in this paper and existing algorithms [17, 20, 21, 47, 57, 60], which show that our algorithms are much better than the existing ones in the numerical experiments.”
• A finite element method for time fractional partial differential equations (2011, methodology): “[17] considered a high-order finite element method for the time fractional partial differential equaions and proved the optimal order error estimates.”
• A modified quasi-boundary value method for an inverse source problem of the time-fractional diffusion equation (2014, background): “, initial value problem and initial boundary value problems for the time fractional diffusion equation have been studied extensively in recent years, for instance, on maximum principle [17], on some uniqueness and existence results [16,33], on numerical solutions by finite element methods [11,13] an”
• An inverse time-dependent source problem for a time-fractional diffusion equation (2016, neutral): “initial value problems and initial boundary value problems for time-fractional diffusion equations, have attracted much more attention in recent years, for instance, in regard to the maximum principle [15], some uniqueness and existence results [15, 28], numerical solutions by finite element methods”