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Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:

Weiping Bu,xiangtan University

Inviter: 唐贻发 研究员
Title:
Space-time finite element method for the distributed-order time fractional reaction diffusion equations

 

Time & Venue:
2020.07.10 09:00-10:00 腾讯会议 ID:373 410 457
Abstract:

直播地址:
https://meeting.tencent.com/s/Lw5rjvCtgX22

In this talk, we propose a space-time finite element method for the distributed-order time fractional reaction diffusion equations (DOTFRDEs). First, using the composite trapezoidal rule, composite Simpson's rule and Gauss-Legendre quadrature rule to discretize the distributed-order derivative and employing the finite element method both in space and time, three fully discrete finite element schemes for DOTFRDEs are developed. Second, for the obtained numerical schemes, the existence, uniqueness and stability are discussed. Third, under the hypothesis about the singular behavior of exact solution near t = 0, the convergence of these numerical schemes are investigated in detail based on the graded time mesh. Forth, in order to reduce the storage requirement and computational cost of these numerical schemes, an efficient sum-of-exponentials approximation is introduced, and the developed space-time finite element schemes are improved. At last, some numerical tests are given to verify the rationality and effectiveness of our method.

 

 

 

 

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