Computational and Applied Mathematics Seminar
Spring 2021
Mondays at 4:10 p.m. via ZOOM talks
(Note the starting time maybe a few minutes later following the adjusted class times on MWF required by the University)
The CAM Seminar is organized in the ISU Mathematics Department. It brings speakers from inside and outside of ISU, raising issues and exchanging ideas on topics of current interest in the are of computational and applied mathematics.
- February 22
Title: A $C^0$ finite element method for the biharmonic problem with Navier boundary conditions in a polygonal domain
Peimeng Yin
Wayne State University
Abstract: In our work, we study the biharmonic equation with the Navier boundary conditions in a polygonal domain. In particular, we propose a method that effectively decouples the 4th-order problem into a system of Poisson equations. Different from the usual mixed method that leads to two Poisson problems but only applies to convex domains, the proposed decomposition involves a third Poisson equation to confine the solution in the correct function space, and therefore can be used in both convex and non-convex domains. A $C^0$ finite element algorithm is in turn proposed to solve the resulted system. In addition, we derive the optimal error estimates for the numerical solution on both quasi-uniform meshes and graded meshes. Numerical test results are presented to justify the theoretical findings. This is a joint work with Hengguang Li and Zhimin Zhang.
ZOOM Link:
Join from a PC, Mac, iPad, iPhone or Android device:
Please click this URL to start or join. https://iastate.zoom.us/j/99184686787
Or, go to https://iastate.zoom.us/join and enter meeting ID: 991 8468 6787
Join from dial-in phone line:
Dial: +1 646 876 9923 or +1 301 715 8592
Meeting ID: 991 8468 6787
Participant ID: Shown after joining the meeting
International numbers available: https://iastate.zoom.us/u/abn9qT9Vc6
- March 01
Title: Nonlocality in nonlinear conservation model
Anh Thuong Vo
University of Nebraska-Lincoln
Abstract: In this talk, we investigate the convergence of solutions of nonlocal conservation PDE to the local counterparts in one space dimension. Nonlocal operators are integral operators that mimic differential operators but account for long-range interactions over a finite horizon. Nonlocality appears in many physical phenomena (fracture, phase separation) and has a wide range of applications (image processing). In Du et al, it was shown that nonlocal operators can be reduced into local operators in a distributional sense. The solution of the nonlocal Burgers equation is also shown to converge to the local counterpart numerically. In our research, we generalize the nonlocal advection operator. In the limit when the horizon parameter approaches zero, we are able to prove nonlocal operator convergence pointwise to its local counterpart. Then, we apply the result to show the convergence of the solution of the nonlocal conservation equation to the local counterpart.
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- March 08
Title:
Xinfeng Liu
University
Abstract:
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- March 15
Title:
Zhongming Wang
University
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- March 22
Title:
Shuwang Li
University
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- March 29
Title:
Rongjie Lai
University
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- April 05
Title:
Robert Basili
Iowa State University
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- April 12
Title:
Wei Zhu
University
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- April 19
Title:
Junshan Lin
Auburn University
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- April 26
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University
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- February 01
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University
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- February 08
Title: Positivity-preserving, energy stable numerical schemes for the Cahn-Hilliard equation with logarithmic potential
Cheng Wang
University of Massachusetts Dartmouth
Abstract:
The Cahn-Hilliard model with logarithmic potential is considered, in which the key difficulty has always been associated with the singularity of the logarithmic terms. An energy stable finite difference scheme, which implicitly treats the logarithmic terms, is proposed and analyzed in this talk. In particular, how to ensure the positivity of the logarithmic arguments, so that the numerical scheme is well-defined at a point-wise level, has been a long-standing mathematical challenge. It is proved that, given any numerical solution with a fixed bound at the previous time step, there exists a unique numerical solution that satisfies the given bound (-1,1) at a point-wise level. As a result, the numerical scheme is proven to be well-defined, and the unique solvability and energy stability could be established with the help of convexity analysis. In addition, an optimal rate convergence analysis could be appropriately established. Some numerical results are also presented in the talk.
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- February 15
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University
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