Keynote Speaker: Zhi-Min Zhang

Abstract:

For 2nd-order elliptic problem, we propose a C1 Petro-Galerkin method, in which kth-order $C^1$-conforming finite elements are adopted for the trial space, and k-2th order discontinuous ($C^{-1}$ or $L^2$) piecewise polynomials are used as the test space. This is in contrast to the classical $C^1$-conforming finite element methods when both trial and test spaces use $C^1$ continuous piecewise polynomials. There is another alternative, using $C^0$ continuous piecewise polynomials as the test space. However, both theoretical analysis and numerical test indicate that $C^1$-$L^2$ pair is superior to the $C^1$-$C^0$ pair in the Petrov-Galerkin method.

The advantage of the $C^1$-$L^2$ Petrov-Galekin method is that it approximates derivatives (gradient) much more accurately than its counterpart existing methods. We prove that at the element nodal points, numerical approximation for both function and its gradient converge at rate 2k-2. We also identify superconvergence points/lines inside elements for function, the first-order and second-order derivatives. Numerical test results demonstrate that our theoretical error bounds are sharp.

Speaker Introduction:

Zhi-Min Zhang, Head of Applied and Computational Mathematics, Beijing Computational Science Research Center (CSRC), Professor and Ph.D. Supervisor, Wayne State University, USA He has been engaged in the research on computational methods for a long time, especially finite element methods, and has made innovative results in the pioneering study of superconvergence, posteriori error estimates, adaptive algorithm, etc. He first established the widely popular mathematical theory of the ZZ discrete reconstruction format and proposed the first discrete reconstruction format based on polynomial conservation. He was and is currently on the editorial board of 9 international computational mathematics journals, including Mathematics of Computation, published more than 180 SCI academic papers and was invited to give a 45-minute speech at the International Congress of Chinese Mathematicians (2010, 2019).

Inviter:

Jiang Xiaoyun Zeng Fanhai Professor of School of Mathematics

Time:

9:30-10:30 on March 25 (Thursday)

Location:

Tencent Meeting, Meeting ID:573 652 252

Click the link to attend the meeting, or add to the meeting list:

https://meeting.tencent.com/s/fIaEVM5HpTXd

Hosted by: School of Mathematics, Shandong University